] As I mentioned in another post- Hamlet is clearly a competent heir, so Claudius has to have the assistance and support of someone else in the governement in order to step into the succession line and it seems as if Polonius is the most likely canidate.

Sari gave us all avery good explanation of how kings were elected in Denmark at the time of Hamlet. Familial succession was not a matter of course. Take a look. It's fascinating. I've linked it below for your ease.