Maybe someone broke into my office and when I get there on Monday I won't be able to work. This is unlikely, but I could look up the robbery statistics for Cambridge and see that this does happen. Mathematically, I should be considering this in making plans for tomorrow, but practically it's a waste of time thinking about it.

I think about such things every time I lock a door. Or at least, I lock doors because I have thought about such things, even if they're not at the forefront of my mind when I do them. Do you not lock yours? Do you have an off-site backup for your data? Insurance against the place burning down?

Having taken such precautions as you think useful, thinking further about it is, to use Eliezer's useful concept, wasted motion. It is a thought that, predictably at the time you think it, will as events transpire turn out to not have contributed in any useful way. You will go to work anyway, and see then whether thieves have been in the night.

Tiny probabilities do not, in general, map to tiny changes in actions. Decisions are typically discontinuous functions of the probabilities.