Here are two very different conceptions of what probabilistic causation is.
(1) It is the probability of causation. When e1 probabilistically causes e2, e1 stands to e2 in the same relation in which one event stands to another when the first deterministically causes the second. The difference between probabilitistic and deterministic causation is just a difference in whether there is (before the effect occurs) a chance that the causal relation will not obtain.
(2) It is the causation of probability. A probabilistic cause causes there to be a certain probability that a certain subsequent event will occur. Nothing else causal happens. It's then a matter of pure chance whether or not that subsequent event occurs. If it does, then, in a plain sense, nothing causes it.
In Libertarian Accounts of Free Will, I suggested that event-causal libertarians had better favor the first of these views, that the truth of the second would be fatal for their position. Indeed, it seems to me that if the second view is correct, and if intentional actions must be caused by psychological states, then events that are "probabilistically caused" cannot be intentional actions.
I haven't seen much discussion of this issue. I wonder if different conceptions of probabilistic causation are sometimes behind different responses to the problem of luck. What do folks think? (I mean you folks!)