What is the difference between rate & probability? Aren't they both calculated the same way? Is the difference then only that rate looks at past events for a period of time vs. probability predicts the possibility of future events?
 A: Rate probably can mean different things, see https://en.wikipedia.org/wiki/Rate_(mathematics)  for an overview, but in this context you probably think rate of occurence of events in some (temporal) random process. 
The rate is simply the expected number of events per some (time) unit (could also be spatial).  That could easily be larger than one, there is indeed no upper limit on a rate, just make the time interval larger, then the rate becomes larger ...
This shows clearly difference from probability. Rate is a kind of an expectation. 
You say that "rate looks at past events for a period of time vs. probability predicts the possibility of future events?". I know of no context that that would be true. 
A: Rates: The instantaneous potential for the occurrence of an event, expressed per number of patients at risk. Rates can be added and subtracted.
Probabilities: A number ranging between 0 and 1. Represents the likelihood of an event happening over a specific period of time.
Briggs, Andrew. Decision Modelling for Health Economic Evaluation (Handbooks in Health Economic Evaluation) (Kindle Locations 958-959). OUP Oxford. Kindle Edition. 
A: The rate is defined is the relationship between numerator and denominator 
probability is a numerator is a part of the denominator, for example, a/a+b   
A: On a temporal frame, Probability usually refers to the expectation of occurrence of an event within a given time span (eg. 5 years), whereas Rate is provided for 1 unit of time (eg. yearly rate).
Converting one to the other goes as follows:
Rate = -ln (1 - Prob) / time
Prob = 1 - e^(-Rate * time)
Consider this example:
A patient with a given disease is likely to evolve from stage I to stage II in 2 years with a probability of 50%.
Does this mean that the probability of that same patient evolving from stage I to stage II of the disease is 100% in 4 years? or does it imply a probability of 150% in 6 years? Certainly not, it wouldn't even be possible.
To answer this question, one must first convert the initial probability into a yearly rate. (Note that this conversion assumes that the rate of occurrence of this event is constant along time.)
Known probability and time (X):
T.x = 2 years
P.x = 0.50
Yearly rate:
R = -ln(1 - P.x) / T.x
= -ln(1 - 0.50) / 2
= 0,346574
Calculated probability in new time frame (Y):
T.y = 4 years
P.y = 1 - e^(-R * T.y)
= 1 - e^(-0,346574 * 4)
= 0,75
So our calculated probability in a different time frame, in this case, would be 75% in 4 years. Or 88% in 6 years, 97% in 10 years, etc.
