Estimate Two Conditional Win Probabilities by Simulation

Three closed doors are labeled 0, 1, and 2. In each trial, exactly one door hides a prize; this winning door is chosen uniformly at random. The remaining two doors are empty. Each simulated trial works as follows: A contestant makes an initial choice uniformly at random from the three doors. The host, who knows the winning door, opens a door that is neither the contestant's initial choice nor the winning door. When both of the other non-winning doors are valid, the host…