A contestant is presented with 4 closed doors. Behind one door is a car, and behind the other three are goats. The contestant picks Door 1. The host, who knows what is behind each door, opens Door 4 to reveal a goat. The host then offers the contestant the chance to switch to either Door 2 or Door 3. If the contestant switches, they will pick one of the two remaining closed doors at random. What is the probability of winning the car if the contestant switches?