Focusing on the chance of success may be missing other factors. You need to also consider their belief in the chance that the problem is real and their belief that someone else won't solve it before them.

Someone who has, say a 30% belief in their ability to contribute to solving a problem will have very different motivations if they're 90% vs 10% confidant that the problem is real (and important) and if they have a 90/10% belief that someone else is going to solve it first.

I doubt it's as simple as multiplying those estimates, but that's an ok place to start.