Was Hitler a "black swan" event? This question was inspired by another question on another SE site: https://history.stackexchange.com/questions/7931/has-any-other-book-in-history-been-as-prescriptive-as-mein-kampf
If someone in 1909 had pointed to a certain 20 year old AUSTRIAN and said, "Within 25 years, this homeless high school dropout will make himself absolute dictator, not of his home country (Austria), but a more powerful neighboring one (Germany)," the statement would have been dismissed as "statistically improbable." Yet, unfortunately, it actually happened.
Suppose the birth of someone like Hitler were a "six sigma" event: I've taken the liberty of "rounding" this to "one in a million." Then, in a world of seven billion people, wouldn't there be 7,000 potential Hitlers around? Then wouldn't the question be not, "do these people exist? but rather, "Will one of these people ever get into power?"
Put another way, does a large enough population offset a "statistical improbability" to a great enough degree so that it becomes at least "somewhat probable"?
 A: The Hitler question (or any similar question) is intractable because there is no good way to say just how improbable something like this is. We don't even know exactly how to formulate the question. That is it could be
"Someone will become dictator of Germany, engage in genocide and attempt to conquer the world"
Or it could add qualifications to the someone ("an Austrian", "an Austrian with little training or education", "an Austrian who was a failed painter" etc.  
Or it could be made more general - "Someone will take over some European country", or even "there will be a massive war, greater than the war from 1914-1918".
It's certainly true that, if something is true of 1 in 1,000,000 people it is true of 7,000 people - indeed, it's true by definition. But you need to be able to say "1 in 1,000,000" vs. (say) 1 in 100,000,000,000,000 . You can do this for some characteristics, if the distribution of that characteristic is known. But historical events aren't subject to this. 
A: There are many different probabilities in here belonging to different questions. Some are small, some are much larger. Some are comparably easy to estimate, some difficult.
I'll consider the "characteristics" dictator, mass murderer/systematic murder and wrote program about that before.
Some rough ideas:


*

*The probability that a given person will become dicator $Pr (dictator | person)$ is small. How large acutally? Maybe some terrorism expert can give you a rough estimation.

*The probability that some person will become dictator of some country $Pr (dictator)$ unfortunately doesn't seem to be that small
Given that I will not become a dictator, this is the more important question for me... hopefully the probability that someone will become dictator of where I actually live is smaller. And I guess that ca. 7 billion people share this view, as opposed to hopefully far fewer people who actually (think to) have non-negligible chances to become dictators and actively work towards this goal.

*The probability that a dicator will murder many people/in a systematic way $Pr (mass~murderer | dictator)$ is uncomfortably high as well.

*(More related the original question) Dictators that wrote some kind of program before seem not to be restricted to Hitler ($Pr (wrote~program~before | dictator) $). Results of a quick browsing through Wiki for candidates whose works could be checked:


*

*Lenin would be a hot candidate (depending on what you accept as prior to coming to power; there's probably something among the 54 vols. of this works).  

*Stalin also wrote already before coming to power

*With Mao I don't know (probably also depends on how you define coming to power)

*No idea when Kim Il Sung wrote his 100 volumes of works

*Whereas Pol Pot and Gaddafi seem to have written when already being dictators. 

*Browsing through a few south american military dicator Wiki pages suggests that they basically didn't write. Or didn't write anything important enough so that someone puts a "works" section into the Wiki page.

*Ther are/were many more dictators....


*Maybe the more interesting question is: How likely is someone writing dictatorial programmes to actually come into power? Or to cause actual trouble?
I guess that would be again a question to be asked to terrorism experts. 
As for the black swans, I think
$Pr (dictator \wedge mass~murderer \wedge wrote~program~before) \approx Pr (mass~murderer | dictator) \cdot Pr (wrote~program~before | dictator) \cdot Pr (dicator)$
isn't orders of magnitude below $Pr (dictator)$, in that respect: no, no black swan (unfortunately! => I don't think that the risk of some dictator somewhere committing mass murder [and having announced it before] is negligible just because Hitler is dead.)
Of course you can add further properties that are required and push the probability towards zero, but I cannot think of reasonable ones right now 


*

*Personally I don't care whether someone murders because of race, hair/skin/eye color, religion, political opinion, place of birth, nationality, illness, completely at random, because of whatever). 

*Also it doesn't really make a difference to me who exactly the person in question is (that is, had it not been Hitler, but Erika Mustermann, we'd ask now whether Erika Mustermann was a black swan). 

*starting a war is maybe a reasonable requirement, but often difficult to judge (maybe it's easier to talk about affinity/getting involved in a war) and it is often a notoriously political question who is actually responsible for a war (think maybe not of WWII, but of Israel./.Palestina or Mali or Libya or who will have started the war in Syriah if the UN gives a mandate for intervention), but my guess is that the correlation between mass murderer and war affinity is high anyways so this additional requirement wouldn't lower our total probability that much. 

A: This question can also be considered from a psychological perspective. Was Hitler a result of the environment? For instance, maybe there would have been a "Hitler" even if Hitler never existed. In other words, the current of the times (the zeitgeist) created Hitler. If this is the case, it is nearly impossible to predict the odds of such an event occurring since there are too many variables. 
Was Hitler a result of his personality? Maybe Hitler would have been Hitler in many different situations. If he was born today, maybe there is a good chance he would become a dictator again. If this is true, we are still faced with an impossible prediction because we do not understand personality well enough and how it interacts with the environment. 
Given these possibilities, and the answers above, it is impossible to calculate the odds of a "Hitler" event since we do not even understand why they arise. Approaching it from a purely empirical standpoint would lead to results that are likely very inaccurate or impossible to interpret. I know the purpose of this question was to simply explore the odds of a very rare event, but we cannot forget the content of the question. I sincerely believe we can predict the destruction of the earth far more accurately than most human-based events that are much less...complicated! 
So you asked: "Put another way, does a large enough population offset a "statistical improbability" to a great enough degree so that it becomes at least "somewhat probable"?"
My answer is we don't know or probably not. The structure of this question assumes partially that Hitler was solely or mostly responsible for his position (e.g., if we have 100 billion people, a "Hitler" should be born again). This is likely not the case, though, and simply throwing a large population at the problem will likely not result in another Hitler. Maybe asking "will the conditions of 1939 be replicated closely in our future" would be of interest, but this would not lead to an answer either!
