A variant of this problem is what led to the longest most hotly debated RHP thread ever, as I recall.

However, you have to assume some things before you answer.

1) Does the host know where the prize is when he has a door opened?

2) Was the host going to open a door and give you the option to switch?

3) Does the host have an interest in whether you win or not, and if so is he for you or against you?

Assuming the problem is the traditional Monty Hall problem, wherein the host does know where the prize is, and was going to give you the option to switch regardless of your initial choice (rendering the third question moot).. The answer is that switching doubles your chances.

The reason being is that it was inevitable the door opened was a losing door, as there is always one available to the host. There was never a chance you'd be staring at a prize knowing you'd picked wrongly at this point, so the chance you picked the right door is still 1/3.

*In the 1/3 of the time we pick correctly, the 2nd door picked is empty 1/1 times.
*

In the 2/3 of the time we pick wrongly, the 2nd door picked is empty 1/1 times, because the choice is not random!

The 2nd door picked is always empty, and (1/3) / (1/1) = 1/3.

However, you do now know the opened door does not hold the prize, and so the remaining door will have the prize the other 2/3 of the time.

Now supposing the person (including the host) that chooses the unchosen door to open first had no knowledge of which door held the prize. In this case, it might be possible that the prize door gets opened, and you would walk way having lost because a swap wouldn't mean anything at this point. Now we are told that the door chosen in fact was empty.

Because it COULD have gone otherwise, our odds of having picked correctly goes up to 1/2. Switching or staying are equally profitable choices in this case.

*In the 1/3 of the time we pick correctly, the 2nd door picked is empty 1/1 times.
*

In the 2/3 of the time we pick wrongly, the 2nd door picked is empty 1/2 times.

2/3 of the time the 2nd door picked is empty, and (1/3) / (2/3) = 1/2.

Now suppose the host knows where the prize is, but bases his choice of whether to offer a switch based on if we pick correctly. Presumably he will count on us to swap doors given the chance, and so whether we ought to swap given the chance depends very much on whether he wishes us to succeed to fail.

If he wishes us to fail, a chance to swap means we have picked correctly.

If he wishes us to win, a chance to swap means we have picked wrongly.