That's not the original phrasing because that's from 1990, have a look at the wiki page you linked. The original problem does not specify that Monty will never

That's not the original phrasing because that's from 1990, have a look at the wiki page you linked. The original problem does not specify that Monty will never open a box with the keys in. The game would still work if this was the case as Monty offers to buy the box before doing so. In the original problem, Monty says the chance is 1/2, which would actually be true if they had opened them randomly. (edit - a game where the host offers to buy the box you have before another one is opened is essentially the end part of deal or no deal). Even the 1990 version however is ambiguous when it comes to puzzles. It just says they open a door which has a goat. The solution originally posted explicitly assumes it to be the case, which is fine.