Resolving the impossible lottery

In a previous post, I have posed a question which seems to admit of two contradictory explanations. Go read that post before this one or this post won't make a whole lot of sense!

Coincidences surprising and inevitable

Kitler photographed by Amy Halligan

Why is it that we might have no problem suspending our disbelief when watching a movie about an alien invasion, but we would find it ridiculous if the writers of a realistic soap opera suddenly started a storyline involving aliens?

This is actually a question that has interested me for some time, even if I seldom gave it much thought.

I will be getting back to the lottery paradox I posed in my last post, but first I have some things to say about the nature of coincidences and improbable events, and this is one of the questions I will attempt to answer.