Your logic makes no sense. How can it switching give you a 50/50 chance of being a winner, when you're saying the door you picked has a 1/3 chance of being the winner
In the event that the third door is eliminated, it is no longer a 1 in 3 shot. The remaining doors (2) are the only ones considered in the second choice, thus choosing between the remaining two (and the only choice to make is to switch) gives odds of 50%.
Hope that helps.