The basics of Jonathan Creek is that there is a set-up that for whatever reason is ‘impossible’. It somehow seems to go against the laws of nature. Jonathan solves it and there is always a non-paranormal explaination. I’m wondering if there’s a series like that in the US, where each setup seems like it couldn’t possibly happen, rather than situations that appear possible frm the start, but then the possibilities get narrowed.
I’m sure the seventies series Ellery Queen used to do “locked room” mysteries of this sort (so named because of the prototypical plot in which the victim is found in a room locked from the inside, with no sign of the murderer).
Perhaps even better would be the series Banacek, in which George Peppard would solve impossible mysteries such as a football player who disappeared after a tackle.
I can’t think of anything on tv that is specifically non-paranormal solutions, but many of the impossible crime novels of John Dickson Carr would have a crime so impossible that it seemed supernatural until his detective explained it away. Carr was an American but lived in England until WWII and most of his novels of the day were set there. He is one of the giants of classic mysteries and he would be known to anyone interested in the field.
Other mystery writers have used this theme. Ed Hoch, the writer of more than 1000 mystery short stories in dozens of series, has several that fall more or less into this scheme including an early series featuring Simon Ark:
Ark is much less well known than Carr’s detectives, though.
Blacke’s Magic Blacke's Magic (TV Series 1986) - IMDb
A magician solves seemingly impossible crimes, almost exactly the same idea.
Anyone besides me remember this one?
Scooby-Doo? 