Difference between probability and possibilty

I’d use probability as a quantifiable, mathematical term. If I spoke about probability, I might be talking about numerical odds or chances: e.g. one chance in six or even Bayesian probability. I don’t use possibility in that way, it is more qualitative.

One way to understand the more slight differences in common meaning is to consider the related words impossible and improbable. Sherlock Holmes said:

"How often have I said to you that when you have eliminated the impossible, whatever remains, however improbable, must be the truth?"

From that, we can deduce:

Impossible - cannot be done

Improbable - unlikely to be done

Possible - can be done (but may be unlikely)

Probable - likely to be done (and likelihood can be measured mathematically)