You can't verify probabilities for any single given event, but you can look at the outcomes for all events for which predicted probabilities were given, and use that to estimate the accuracy of the methodology/models used.
So, for example, when 538 said that Trump had a 30% chance of winning, its hard to say how accurate that was given it was a one time event. But if you look over all of their election predictions, and look at those they predicted to win 30% of the time, about 30% of them should have been victories (with some margin for error, of course). If 50% were victories, or only 10%, then maybe that would indicate their models aren't doing so hot.
So, for example, when 538 said that Trump had a 30% chance of winning, its hard to say how accurate that was given it was a one time event. But if you look over all of their election predictions, and look at those they predicted to win 30% of the time, about 30% of them should have been victories (with some margin for error, of course). If 50% were victories, or only 10%, then maybe that would indicate their models aren't doing so hot.