Probability Riddle

My initial thoughts were as follows:

Probability Principles:
Bayes' Rule

The probability of A and B equals the probability of A, given B, multiplied by the probability of B.

P(A,B) = P(A|B)*P(B)

With the given information, you automatically know that all the doors have the same probability, 1/3. Next, you are given additional informaiton, which will have an outcome on the solution, hence, where Bayes' Rules comes into play, stated above.

Now, the probability of A, given that door C is wrong, is 1/2. Also, at the same token, the probability of B is just straight up, 1/2. This means that P(A|B) = 1/2, and P(B) = 1/2, therefore, P(A|B)*P(B) = 1/4.

This shows that by switching, you now have a new probability of 1/4 opposed to the initial probability of 1/3 you had in the beginning.

This, however is wrong, but my professor is still yet to give me a concrete answer on why... Asshole.

Who knows, maybe I proved hundreds of Mathematical geniouses wrong!