Considering we all know about Monty Hall Problem of $2$ Goats and $1$ Car. Also, the solution of the probability $2/3$ concentrating on a single door.
Now, an alternate approach can be as follows:
Consider a person $A$ and doors $1,2,3.$ Now, also consider another person let say $B$.
$B$ comes into consideration only after Monty has shown the door behind which there is a goat.
Let's say $A$ always switches its door. $B$ selects the door which was previously selected by $A$.
Now in this scenario, as we say $A$ has probability $2/3$, whereas $B$ has probability $1/3$ of selecting door with the car.
But the problem is person $B$ comes into consideration where he has only $2$ choices one with the car and one with the goat, his probability of getting a door with the car behind should be $1/2$ and not $1/3$.
What am I missing here??