I'd say the door would be 2/3 in favor of being a 1/2 shot. So 2/3 x 1/2 = 2/6 = 1/3 for switching? Which would be the same as not switching. That doesn't mean 50/50, because a third of the time the removed door would be the winner.

And in the spirit of the problem, the host couldn't show you what's behind the randomly removed door because if it was the winner you wouldn't need to switch, and switching's the whole point of the problem.