Death in Paradise

This is a British TV Police drama, but has a much lighter tone than the rest and reminds me of Agatha Christie's novels. A British police detective has been sent to the Caribbean in order to help train some of their staff, but ends up having to stay there long-term. The series definitely has an emphasis on comedy, but it's also a quite fun guessing and theorising who you think the killer is. There is a new death in each episode that the team has to work out who did it, with only a small range of suspects, usually around 5. The team then investigates, and gathers clues, until the detective always has a breakthrough where no one knows what he's thinking. He then gathers up the suspects and eliminates them one by one until revealing how committed the crime.