Jogee I think you're pretty close . The way I look at it is :if we choose door #1 we would all agree that the probability of winning the car is 1/3 and if the host always reveals a goat from behind the remaining 2 doors then by switching our odds would be 2/3 . Another way of looking at it would be if we choose door #1 and we agree that it has a 1/3 chance, which in turn means that there is a 2/3 chance that the car is not behind door #1 and if the host removes an incorrect answer from the remaining 2 doors the odds are 2/3 by switching .
We can set up a small game to prove this . Take 2 jokers and an ace from a deck of cards, let the ace represent the car . Have a partner lay out the three cards, then you pick 1 of the three, record whether you won (got the ace) or lost (got the joker), do this like 30 times . Next have your partner lay out the cards in the same way, make your pick, but this time have your partner reveal a joker from the remaining 2 cards, then switch from your original choice to the card that is left, do this 30 times and record the results .
Larry