"Possibility" means something may happen, but we don't know how likely. "Probability" means something may happen, but we believe it is more likely (i.e., more "probable") than not. So I could say there is a possibility of rain next week; but I think there is a probability of rain tonight, because I can see dark clouds and detect a change in the barometric pressure.

In several contexts (not always), /possibility/ has a positive meaning, like: "answer to that insertion, seems a possibility to you"; You may stick a number to /probability/, usually like a percentage (in this case 100 % means: sure event), or as a fraction of unity (in this case 0.5 means an equal chance of the event to verify or not). You can't stick a number to /possibility/. Examples: The probability of rain within the next 5 hours is 95 % The probability of rain tomorrow morning is 65 % from the data available now.