None of the explanations in the article really convinced me either. But after looking at the chart of all possible outcomes for a while, it finally clicked. It makes more sense to think of it in reverse from the winning position.
Winning by switching doors requires your first choice to be incorrect.
You have a 2/3 chance of guessing incorrectly when all three doors are closed.
Thus, you have a 2/3 chance of putting yourself in the position from which switching will win.
Winning by switching doors requires your first choice to be incorrect.
You have a 2/3 chance of guessing incorrectly when all three doors are closed.
Thus, you have a 2/3 chance of putting yourself in the position from which switching will win.