It didn't seem right to me at first, so I worked through it. The trick was to realize that switching always gives the opposite result of the initial choice. So if the initial choice is correct, switching will make it wrong. On the other hand, if the initial choice is wrong, switching will make it right. (Recall that Monty eliminated one wrong choice, so there is only one other choice from which to choose.) Since you have 1/3 chance of being right and 2/3 chance of being wrong on the initial pick, switching will reverse your odds.