In real life, you are not ever supposed to have a prior improbability of 10^-100 for some fact distinguished enough to be written down, and yet encounter strong evidence, say 10^10 to 1, that the thing has actually happened.

Sure you do. As you pointed out, dice rolls. The sequence of rolls in a game of Risk

Those aren't "distinguished enough to be written down" before the game is played. I'll edit to make this slightly clearer hopefully.