The answer isn't difficult: First we ask how probable it is that George utters a true statement and Bill makes a true statement of support. Since they both tell the truth 1/4 of the time, these events will both turn out to be true 1/16 of the time (1/4 x 1/4). Now we ask how probable it is that Bill will make a statement of support. Since Bill will utter his support when either both he and George tell the truth or when they both lie, the probability of this is 10/16 (1/4 x 1/4 + 3/4 x 3/4). Thus the probability that George is telling the truth given that Bill supports him is 1/10 ( the ratio of 1/16 to 10/16).
The moral: Confirmation of a very dishonest person's unreliable statement by another very dishonest person makes the statement even less reliable.
(Adapted from the writing of John Allen Paulos. Partisanized by me.)