Final answer:
The correct answer to the question is Columbo, the rumpled police detective whose wife, although never seen on his show, received her own show titled "Kate Loves A Mystery".
Step-by-step explanation:
The wife of the rumpled police detective referred to in the question who was never seen on his show but had her own show called "Kate Loves A Mystery" is from the television series featuring Columbo. Columbo is the correct answer, which is option a). Unlike the detective Sherlock Holmes who was the product of Sir Arthur Conan Doyle's imagination, Columbo was a television character portrayed by actor Peter Falk. Columbo's wife was an unseen character on his show, but later had her spin-off series.