“Plausible Detective” has two components, in my opinion:
#1: perhaps most importantly, the ‘detective’ (i.e. the central character in the book who solves the crime) should be in a profession which renders said central character likely to discover crimes. Police or private detective are the obvious plausible jobs, but emergency response professionals are options, as is reporter. The world being what it is, just about anyone can stumble across a crime or three, but more than that and the author had probably come up with a good explanation for why the person keeps stumbling across crimes.
#2: people living in urban or populous areas are more likely to encounter crime–not because cities are more criminal but simply because there are more people to commit crimes around.
My favorite example here (for certain meanings of the term) is Lilian Jackson Braun’s “The Cat who…” series. When Qwilleran was a newspaper reporter living in “Down Below”, the series’ term for (probably!) Detroit, he might well come across dead bodies on a regular basis. Once Braun moved him to Pickaxe, and gave him a fortune sufficient to allow him to never work again…well, one might guess that the body count would drop dramatically. Not so. Instead, Moose County almost certainly rivals Rita Mae Brown’s Albemarle County for world’s highest per capita crime rate. I happen to like both series, although as per my previous blog post, I think both authors should have stopped at 6, but then I like character driven books with a fair bit of detail about places I’ve never been. And I like cats; it’s interesting to read Brown’s take on what animals think of us.
Some connection to the police and a talent for detection further the plausibility of the series a great deal, however. A reasonably talented writer can create a plausible detective from the most unlikely sources; who’d have thought that an elderly dithering spinster from a backwash English village would become the archetypal female detective of mature years? Even a cloistered monk might do if it turns out that he has a talent for what passes for forensic detection in the fourteenth century. Miss Marple and Brother Cadfael have both a connection with the police, and an unsuspected talent for detection.