The request is asking for a suitable substitute for evident, where, rather than suggesting something is a fact that is obvious, it suggests something is a fact that not only is not obvious, but that it requires the powers of mind and observation that someone like Sherlock Holmes would possess.
The word that I found most fitting to these conditions is abstruse (Wordnet Dictionary):
difficult to penetrate; incomprehensible to one of ordinary understanding or knowledge;
Another definition (Dictionary.com):
hard to understand; recondite; esoteric:
Recondite (Dictionary.com) would be a very good alternative, with nearly identical meaning:
dealing with very profound, difficult, or abstruse subject matter; beyond ordinary knowledge or understanding; esoteric; little known; obscure
I found this entertaining article (Vocbulary.com), which I think captures the meaning very well, and I’ll quote it fully:
Abstruse things are difficult to understand because they are so deep and intellectually challenging. It might be hard to figure out how a toilet flushes but the technology that goes into making the Internet function is abstruse.
The Latin roots of the word abstruse are about concealing or hiding something, which is a good way to remember the meaning of this word. It is useful when describing something that is overly confusing, or if someone is deliberately making a story or a situation more complicated than necessary. It sounds and looks like obtuse, but abstruse is almost its opposite. Obtuse is dull or lacking a sharpness of intellect. While Abstruse is president of the chess club, Obtuse is hanging out by the parking lot smoking cigarettes.
As far as Sherlock Holmes is concerned, I found the following quotes from some of the collected works by Arthur Conan Doyle:
From The Sign of Four
“My mind," he said, "rebels at stagnation. Give me problems, give me work, give me the most abstruse cryptogram or the most intricate analysis, and I am in my own proper atmosphere. I can dispense then with artificial stimulants. But I abhor the dull routine of existence. I crave for mental exaltation. That is why I have chosen my own particular profession, or rather created it, for I am the only one in the world.”
Here, from The Naval Treaty, is one that may have special meaning to some
“Oh, the mystery!” he answered, coming back with a start to the realities of life. “Well, it would be absurd to deny that the case is a very abstruse and complicated one, but I can promise you that I will look into the matter and let you know any points which may strike me.”
“Do you see any clue?”
“You have furnished me with seven, but, of course, I must test them before I can pronounce upon their value.”
“You suspect some one?”
“I suspect myself.”
“What!”
“Of coming to conclusions too rapidly.”
The character Dr. Gregory House, of the U.S. television program House, (hat tip to Mari-Lou A) has a Holmes-like pit-bull tenacity (with all the same scariness to some) for resolving deadly afflictions. He was described in an article of the Los Angeles Times (Patt Morrison, July 20, 2012) this way:
His cause wasn’t the patient; it was solving the puzzle of what was killing the patient. Some of the abstruse ailments he diagnosed were probably a footnote on Page 1063 of a textbook in a real med-school class taught at 8 o’clock on a Monday morning, but no matter. Hypochondriacs of the world swooned.