TITLE: Four men, hats and probability
QUESTION [15 upvotes]: I encountered the four men in hats puzzle for the first time today. My question is about a realisation I (think I) had while arriving at the solution, but I have no idea whether I've made a mistake somewhere.
Before I got to the actual answer, I was thinking about each man's chances of correctly guessing his hat colour. My thought process went something along these lines:

At first blush, D has the best chances, as he can see the most.
Hang on - D has only a 1 in 2 chance, the same as anyone else.
Anyone else? No - C can see that B has a white hat, so he knows there's only one other. It can be on one of three heads, so if he guesses that his own is black, his chances of being right are 2 in 3.

What threw me about this, assuming that last realisation isn't flawed in some way, is that D can also see that B has a white hat. Somehow, C has a better chance of being right, even though D (in some sense) has more knowledge, at least for this configuration of hats.
What am I missing?
UPDATE
Thanks for the answers so far. I don't think I was very clear on what I was asking though: I did manage to solve the puzzle, but what confused me was the realisation I outlined above while getting there. Forgetting the original goal of the puzzle (how do the men reason about the solution) and only taking into consideration their chances of successfully guessing, how do I explain the fact that C's chances seem better than D's, even though D can see everything that C can, and more?

REPLY [3 votes]: C knows that  B is white. If he where white D would of called out Black. However, he doesn't so C knows D is confused. So C must be Black.