I'm almost certainly assigning this more emotional weight than the very tiny probability that is at all justified.

I don't know about you but the emotion I associate with the possibility is fascination, curiosity and some feeling that we need a word for along the lines of entertainment-satisfaction. It's just so far out into far mode that it doesn't associate with visceral fear. And given the low probability it is one instance of disconnection of emotion to knowledge of threat that doesn't seem like a problem! :)