In my paper with Aaron and Nate, we were getting probabilities such as 5e-85 or 9e-16 from our normal-distribution model. Sure, the probability that a vote in D.C. would be decisive was low, but 10^-85? No way. So we switched to a t_4 distribution, which smoothed these probabilities down to 2e-12 and 2e-10. Not perfect, I’m sure, but more plausible.
Just remember: don’t be a slave to your model. Work with it. Taking a model too seriously is really just another way of not taking it seriously at all. (By this I mean that, if you say you really believe a probability such as 10^-85, what you’re really doing is devaluing the concept of belief in probabilities, and I’m thinking that will leak back and corrupt all the other probabilistic statements you make.)