Turning to door B, initially was unopened and

you had a one-third chance of the sports car being behind it.

My opening of door B, revealing the goat did give you some new information.

And indeed now you know what is behind door B.

So armed with that new data,

that new information, you were able to revise or update this probability.

In this case, the revision is downwards.

It was originally a third, and now becomes a probability of 0,

an impossible event because we know for a fact the goat is behind there.

So now let's turn to door C.

So if I ask you the question, did you learn anything about door C?

Many people would probably answer no,

because they see the action of door B being opened.

However, you have to be conscious that I have the option of opening door C.

It was only door A, which had to remain closed.

So in fact, your seeing me reveal the goat behind door B, simultaneously,

you are actually observing me consciously choosing not to open door C.

So in fact, you do learn something about door C.

So let's consider, the two possible explanations for

why I opened door B in the first place.

Let's imagine the sports car was behind door A, you choose it and

therefore there are goats behind doors B and C.

I can't open door A and therefore, which ever door B or

C I open, I would be revealing a goat.

And in this world therefore,

I am indifferent between opening door B or door C.

So that is one possible explanation.

Of course, the other explanation is that the sports car is behind door C.

Your choosing of door A prevents me from opening it, clearly I'm not going to show

you where the sports car is initially, so I'm not going to be opening door C.

And it's the only option available to me is to open door B.

Now as I know where the sports car is,

I know which of those two explanations is the correct one.

Of course though, you do not.

So you know that there's a possibility that I was forced to open door B,

and that original probability of a third that you assigned to door B

is in fact transferred and inherited to door C.

And hence, its revised probability

of having the sports car behind it is now two-thirds.

So the original probability distribution of a third, a third, and

a third is now revise to a third, zero, and two-thirds.

Now I'm a nice guy, so knowing this new information,

let me return the decision back to you.

These are now your revised probabilities of winning the sports car.

So I'm guessing none of you is going to choose door B.

So think about whether you would choose door A or door C.