With the aim of making this question/answers post self-contained, I've inserted the image from the linked puzzle, below, followed by the solution given in that link.
Four Men and a Hat
Shown above are four men buried up to their necks in the ground. They cannot move, so they can only look forward. Between A and B is a brick wall which cannot be seen through.
They all know that between them they are wearing four hats--two black and two white--but they do not know what color they are wearing. Each of them know where the other three men are buried.
In order to avoid being shot, one of them must call out to the executioner the color of their hat. If they get it wrong, everyone will be shot. They are not allowed to talk to each other and have 10 minutes to fathom it out.
After one minute, one of them calls out.
Question: Which one of them calls out? Why is he 100% certain of the color of his hat?
This is not a trick question. There are no outside influences nor other ways of communicating. They cannot move and are buried in a straight line; A & B can only see their respective sides of the wall, C can see B, and D can see B & C.
Spoiler/solution, and see Steven's answer for clarification
C calls out that he is wearing a black hat. Why is he 100% certain of the color of his hat?
After a while, C comes to the realization that he must answer. This is because D can't answer, and neither can A or B. D can see C and B, but can't determine his own hat color. B can't see anyone and also can't determine his own hat color. A is in the same situation as B, where he can't see anyone and can't determine his own hat color. Since A, B, and D are silent, that leaves C. C knows he is wearing a black hat because if D saw that both B and C were wearing white hats, then he would have answered. But since D is silent, C knows that he must be wearing a black hat as he can see that B is wearing a white hat.
The 100% certainty possessed by C is a function of the meta-knowledge possessed by the men. Each man knows that each man is wearing 1 of 4 hats, 2 of which are black and two white. Each man's life is at stake, so we can assume each knows well enough (or figures out) not to shout out carelessly to "guess" the color of his hat.
Assume the given distribution of hats and positions. Suppose that their lives are not at stake...That each is simply asked to guess the color of his own hat, and asked to call out his choice of color simultaneously in chorus with the others. Then we can determine the probability that any given man has of guessing correctly; as the OP suggests, C has the greatest probability of being correct, though in this challenge scenario, C can not be certain (since he can learn nothing from the silence of the others in this situation.
My conjecture: If $P(X)$ denotes the probability that X guesses correctly, then
$$P(A) = P(B) = P(D) = 1/2 < P(C) = 2/3$$
Note: Of course this depends on the distribution of hats as shown in the image above, for if they are distributed such that B and C are each wearing the same colored had, then D would see this, and thus be able to assert, with certainty ($P(D) = 1.0$) the color of his own hat.