This is of course exactly right. Just as a bizarre example: When I was a teenager, one day I was a passenger in two unrelated, non-weather-related automobile accidents, with two different adult drivers (who were parents of friends). The odds of that happening, estimated at the time I got up, must have been astronomically small. But once the first accident happened, the odds of the second accident happening were no different than they would have been had the first one not happened.