How does The Crucible answer the question of how someone whose special knowledge is called for would respond to a situation?
Reverend Hale has developed a specialty in the occult. He is the best and, perhaps, only figure in the play relatable to the question at hand, but he certainly suggests a number of answers to that question.
Hale responds to his invitation to investigate the situation in Salem with skepticism initially. He is not sure that the people in Salem will recognize his expertise or his right to be involved in the happenings of Salem. When he is assured that his expertise is recognized, he begins to act rather proudly, demonstrating his knowledge and making decisions with authority.
We see in Hale's actions at least two dynamics. First, he is willing to do the job he is qualified for - or that be believes he is specially qualified for. He steps into the fray, as it were, because he feels that it is his duty to do so. Second, Hale is elevated to a position of authority and status due to his expertise. This elevated position leads quickly to a moral corruption - a very human response - as he begins to act with a rather blind confidence that defies reason (as we see when Proctor tries to reason with Hale in the second act and fails).
Hale embodies many of the moral contradictions of the play: he is a man of integrity who, although at times misguided and overzealous, is willing to change his mind when confronted with the truth. (eNotes)
Some of Hale's behavior and posturing are certainly a result of his perceived expertise.