Can someone tell me what are the chances of scanning the same base twice within roughly 24 hours?

1/x x being the total number of bases in the game, there is a more concrete number buuuut I don't really feel like finding out

That equation would more likely be 1/(x-y) where x is as you said and y is the number of bases currently locked.

But for ships the longer you are disabled before you repair, then when you repair you show up more readily on the bt, so it may be similar for bases.

I have personally locked the same base twice in a day. So part is relevant to your bases' level. We as a level 8 never see below a 4. Part is who is currently locked. The rest is luck and how many reds you want to spend to keep hunting someone down.

If your question is purely pedantic.. i think the formulae already listed is prolly as decent a guess as there is known.

I know that when I've been scanning for a specific base, there have been times where I scan ANOTHER base multiple times. i.e.: I'm looking for base A, but base B shows up 2 or 3 times in 100+ scans in a single session.