Since the host will never open a door with the car behind it, the remaining door will have a car behind it in exactly those cases where you originally pick a door with a goat behind it. Since there is a 2/3 chance of you originally picking a door with a goat behind it, there is therefore a 2/3 chance that the remaining door has a car behind it.

If you don’t know what I’m talking about, you can find the Month Hall problem described in the movie 21 or the TV show Brooklyn Nine-Nine. You can find longer explanations of it over at D!NG, Vox, and Numberphile.