How to get away with Murder

The show I'm currently obsessed with on Netflix is How to Get Away With Murder. (The show is about a lawyer who solves murder cases and it tells you what the person did wrong. This show does not actually just list ways on how to get away with murder.) While I was studying for my exams I took a break and watched an episode. I had just finished studying Hamlet for the day. All i kept thinking about was how perfect Claudius executed the murder of Hamlet Sr. He made it seem as if poison killed the king and made sure no witnesses were around, so he thought. Claudius got caught because of 3 things. 1) He had the motive: If there was any inkling of suspicion that Hamlet Sr's death was murder, his brother could be a very eligible candidate because of the crown. Claudius wanted to be king so bad that he killed his brother.  2) The wife: Every murderer likes to keep some sort of trophy from their victim. Claudius took his brother's wife. If he didn't want people to suspect him, he should have kept his distance from Gertrude, at least for a bit longer than only one month. 3) The witness: So obviously the one person who knew Claudius killed the king was the king himself. They didn't teach me how to deal with the dead coming back in How to Get Away with Murder, but they do teach you to get rid of all the evidence and witnesses are evidence.