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Dorikka comments on Practicing what you preach - Less Wrong
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P(X is true | someone who I consider well-educated in the field of interest stated X is true) > P(X is true)
Restating your argument in the form of a Bayesian probability statement isn't going to increase its validity.
P (X|{affirming statement by authority in subject of X}) == P(X).
It has no bearing, and in fact is demonstrative of a broken heuristic. I'll try to give another example to explain why. An expert's expertise in a field is only as valid as his accuracy in the field. The probability of his expertise being, well, relevant is dependant upon his ability to make valid statements. Assigning probability to the validity of a statement by an expert, thusly, on the fact that the expert has made a statement is putting the cart before the horse. It's like saying that because a coin has come up heads every time you've flipped it before it's now likely to come up heads this time.
I'm puzzled and wonder if I'm missing your point because this update makes perfect sense to me. Let's say that I start for a prior for whether the coin is fair, P(fair), a prior for whether it is biased towards heads, P(headbiased), and a prior for whether it is biased towards tails P(tailbiased). My updated probability for P(headbiased) increases if I get lots of heads on the coin and few or no tails. It'll probably help if we understand each other on this simpler example before moving on to appeals to authority.