Where the Odds Go

Here is the mechanic in slow motion. The moment you pick, you lock in a 1/3 chance of being right and a 2/3 chance of being wrong. The host opening a goat door does not touch your 1/3 — that number is frozen the instant you chose.

So where does the 2/3 live now? It cannot vanish. With the goat door gone, it has only one place left to sit: the door you did not pick. Switch and you claim it.