Assuming college professors are an intelligent lot, the first one would have known that he had on a red hat if the other two both had green hats. But since he didn't know, we can assume that he saw at least one red hat. This gives the following possible combinations:

The second professor then knows that the first saw at least one red hat.If the second professor saw a green hat on the blind professor, he would have known the he himself had a red hat.However, he stated that he did not know the color of his hat.This could only mean that he saw a red hat on the blind professor.

Thus, the blind professor reasons to himself, "The first professor would have known his own color if he saw two green hats -- but he didn't. The second professor would have known his own color if he saw a green hat on my head -- but he didn't.If he didn't see a green hat on my head, he must have seen a read on."

So the blind professor wins the prize.