The fallacy of singling out a particular hypothesis for attention when there is insufficient evidence already in hand to justify such special attention.
To see the problem of privileging the hypothesis, suppose that the police in Largeville, a town with a million inhabitants, are investigating a murder in which there are few or no clues - the victim was stabbed to death in an alley, and there are no fingerprints and no witnesses.
Then, one of the detectives says, "Well... we have no idea who did it... no particular evidence singling out any of the million people in this city... but let's consider the possibility that this murder was committed by Mortimer Q. Snodgrass, who lives at 128 Ordinary Ln."
If the detective does not have evidence already in hand to justify singling out Mortimer for such special and individual attention, then this is, or ought to be, a violation of Mortimer's civil rights.
This is true even if the detective is not claiming that Mortimer did do it, but only suggesting that all the police officers consider that Mortimer might have done it. The principle of locating the hypothesis says that it often takes more evidence to first distinguish the true hypothesis as worthy of explicit consideration, than to distinguish among the remaining alternatives. So the detective is jumping over the job of providing most of the evidence that would have to be brought against Mortimer.
"Privileging the hypothesis" is the fallacy committed by a creationist who points out a purported flaw in standard evolutionary theory, and brings forward the Trinity to fill the gap - rather than a billion other deities or a trillion other naturalistic hypotheses. Actually, without evidence already in hand that points to the Trinity specifically, one cannot justify raising that particular hypothesis to explicit attention rather than a trillion others.
The anti-work of anti-epistemology is to manufacture belief without evidence, and in large answer spaces, attention without evidence is more than halfway to belief without evidence. Someone who spends all day pondering whether the Trinity does or does not exist - rather than Allah, Thor, or the Flying Spaghetti Monster - is more than halfway converted to Christianity.