For quite awhile, I included shows about private investigators in my legal dramas category. But eventually I decided to spin private eyes off into their own category. There can still be overlap, of course. Shows in this category, which focus mainly on private eyes, very often also involve police. Whereas shows that I leave in the "legal dramas" category focus mainly on police and/or lawyers. (Of course shows about police are often specifically about police detectives, so there can definitely be a lot of similarity to the work done by private detectives. But the difference is that shows in this category are about people who don't work for official organizations.) And... I guess I may also include a few shows that are about individuals who take on cases to help people in ways that at least partially involve P.I.-type work, but aren't exactly private eyes, but rather... eh, something harder to clearly define.
See also crime fiction, mystery films, and noir episodes