It’s called toilet plume.
A toilet plume is the invisible to the naked eye, cloud-like dispersal of raw, infectious sewage particles as a result of flushing a toilet. Flush particles rapidly rise out of the bowl and several feet into the air after flushing. Aerosolized droplets can remain suspended in the air for tens of minutes between users, posing an inhalation risk. These invisible particles go on to coat and spread onto surfaces like floors and counters or objects like hand towels, bathmats, or even toothbrushes.
Someone’s done the math though it rests on some challengeable assumptions about dispersion over time, moreover agnostic of location. The thing is that with those more basic assumptions the probability is about 99% per deep breath, so much higher chances for at least once in a lifetime, enough to consider it probably true even if real-life dispersion isn’t as good as the basic assumption taken. John Allen Paulos (Temple U mathematician) was the first one to get the ball rolling on this idea that I can remember, in his Innumeracy book. Interesting read, btw.
Interesting! Noted for my next bookshop visit :)