Just to clarify: are you categorically denying the reality of broad categories? Or is there a more subtle point here that deals more with positive feelings?

One of the probabilities that's being used here is actually the probability that something is possible, and I think that needs to be taken into account.

Let's structure this as a game, and allow you infinite tries to win the prize. You've set the probability of winning at some insanely small fraction of a percent, but that doesn't matter because you have infinite time. Given enough plays, you should win the prize, right?

Not necessarily. Let's say that if the game is possible to win, there is a 99.99% chance of winning, and that the relevant probability in calculating the chance of winning is whether the game is winnable. In that situation, you could play the game infinitely and still lose. In the same way, you could take up this offer infinite times and never win 1,000 quadrillion happy days.

Because of this, if one of the probabilities is that something has a low chance of existing, you shouldn't play the game.