They're totally, utterly, different and totally unrelated.
A "propensity" is a quality of a person.
For example, I have a propensity to drink too much, I have a propensity to post on the ELU site, I have a propensity to get drunk (mentioned that one!), you have a propensity to watch sci-fi movies, etc etc.
"Probability" is a mathematical term and is just totally unrelated.
It has nothing at all to do with describing a person's propensities.
So, the probability of tossing heads is 50%, smokers have a 73% probability of cancer, I have a 88% probability of liver damage, etc etc.
"Propensity" is a quality of a person - simply, it relates to their choices in life.
(Your particular example perhaps leads to confusion, because, the sentence happens to include "a person" in the sentence. But notice it is totally unrelated to their propensities - i.e., "things they like to do / usually choose". You're just stating a mathematical probability. "Research shows that for his habits, he has a 82% probability of contracting cancer.")