1% of the global population means roughly 1% in my country? Assuming that you hear that X affects 1% of the global population, is it safe to assume that it should affect 1% of the population of your country/city/subgroup?
Given that there is nothing in the subgroup to affect the distribution of X. (Assume that the distribution of X is not mentioned, so should we assume normal/Gaussian?*)
I'm asking because, often, I hear X disease is very rare, it only affects 1% of the global population, which sounds HUGE to me.
*if so, you could say that your country is an outlier and it's much less that 1%, but on average, you should be correct, right?
 A: Very few things are independent of world location. In particular in disease, if someone says that it affects x% of the world population, it is very likely localized. For example: most Malaria is confined to a latitude range (there isn't much in northern Europe for example). And many genetic diseases fall within populations with identical genetics - therefore they affect certain locations more than others. 
So, no. 
A: The accepted answer is good, but let me generalize the concept to make it clearer.
In order to assume that probability of a characteristic in a sample (e.g. country) is the same as probability in the whole population (e.g. world), the sample needs to be representative of the whole. Would it be valid to say "X% of country A -> therefore X% of global population"? (For some characteristics, that might be true, but not for most things.) If not, then it's also not valid to go the other direction and say "X% of global population -> therefore X% of country A". 
A: There are too many counter examples that make your premise false. Asians have a far lower rate of diabetes than Americans, for example. Yet, a second generation Asian in US has similar rates. Not genetic, then, but habit, diet. It would surprise me if any disease had a mathematically 'nice' spread across the world. 
To offer a money counter example, US median income is equal to about top 1% number for world income. 
