This is precisely the first subtility you encounter when you learn probabilities : they are not identical. Paul is right that the formulation of the question doesn't refer to the Monty Hall problem at all, this isn't the same algorithm. But in this case, the probability turns out to be the same. That's the real confusion in Jeff's article.

I mean, it's not even my own deduction, it's what you are taught when you learn probabilities. It's a basic and core paradigm, and I'll digg it up from Wikipedia if somebody still doubts it :)