Earlier quoted context omitted.
I wrote out a hopefully helpful intution down below [0]. Here's a terse part of it: > Or just imagine monty hall with infinite doors. I'm thinking of a number between 1 and infinity (secretly, it's 19083412039102388171230123). You pick a number, and then I'll narrow down your choice to two options. Do you think you just happened to pick my number, or do you switch? You're right that it's absolutely the narrowing down…
Ok. But you picked a very very very very small number between 1 and infinity. That can’t be random.
That it isn't random is precisely the point, isn't it?
The only difference that the "very very very very small number" makes is that the odds aren't infinity to one but two to one. Still winning odds.