Here’s a very simple explanation. You pick door 1 and since there is a 1/3 chance of picking car, then there must be 2/3 chance that car is behind door 2 or 3. When Monty shows you door 2, he will never show you the car. Thus, he just spilled the beans, that is the odds of the car behind door 2 or 3 is still 2/3, but since he showed it is not door 2, the odds that it is just behine door #3 is 2/3.
Here’s the definitive explanation and simulation from nerds at UCSD math dept. Monty knows where the car is and that is why the odds from switching is 2/3. (He never open up the door with the car)
