Some people think that for C to explain E, P(E|C) must be high. This is false. Suppose two events E1 and E2 have probabilistic explanations, and we understand that the events are independent. Then we understand why E1 occurs and why E2 occurs, and we also understand why their conjunction occurs. But of course their conjunction has lower probability than either of them, and iterating this argument we get to a conjunctive event such that we understand why it occurs even though its probabilistic explanation is a quite low probability one.