Win a Car Game Show

You are in a game show. The purpose of the game show to correctly guess behind which of three doors lies a fancy car - your prize if you win. Behind the other two doors lie some goats. The game show host first asks you to guess one door, then - without showing you what lies behind your door - shows you another door with a goat behind it. He then asks whether you want to switch your guess from your original door to the other remaining door. Should you switch, and what is the maximum probability that you would win the car?

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