After enumerating all the options and their respective probabilities, yes, you discard all those that are inconsistent with the information to hand.

You bring up the Monty Hall problem. The options there are:

    [ c ] [ g ] [ g ]
    [ g ] [ c ] [ g ]
    [ g ] [ g ] [ c ]

These are all equally likely.

Then you choose a door. Let's assume you choose door 1. To keep things equally likely, let's suppose Monty flips a coin. Heads he opens the left-most unchosen door that doesn't reveal a car, Tails he opens the right-most. Now we have six options:

  Heads:
    [ c ] [ g*] [ g ]
    [ g ] [ c ] [ g*]
    [ g ] [ g*] [ c ]

  Tails:
    [ c ] [ g ] [ g*]
    [ g ] [ c ] [ g*]
    [ g ] [ g*] [ c ]

As you can see, there are now 6 equi-probable choices, and in 4 of them it's better to switch.

A: So now let's take another experiment. I tell you I'm going to flip two coins until at least one of them is heads. I do that. Now I ask you to bet on whether or not there is a tail. What do you think are fair odds?

B: Now I hunt among couples with two children until I find one that doesn't have two girls, and I ask: what are the odds they have two boys?

C: Finally, I hunt among couples with two children until I find one that has at least one boy, and I ask: what are the odds they have two boys?

This last is how the question is usually interpreted.

There are three options.

1: Your answers to A, B, and C are not all the same;

2: They are all the same, and not 1/3;

3: They are all the same, and all 1/3.

If your answers to A, B and C are not all the same, I'd like to know why. If they are not all 1/3, I'd like to play game A with you. If your answer to C is 1/3, then you've agreed with the usually interpretation and contradicted yourself.