Switching the door increases your chances of finding the coin!

Why? Initially, the chance of finding the coin behind your first chosen door was only 1/. In contrast, the chance that the coin was behind any one of the other doors was /. After eliminating all but one of these other doors, the probability of the coin being behind the remaining unchosen door is now higher than your original door, making it the statistically better choice to switch!

Therefore, after switching, the probability of finding the coin is /