0xp I don't have a problem believing the unusual rules for succession (odd rules of various types have cropped up often through history), but so far, the information given is really just a sketch of the idea. A greater level of detail would be desirable.

As it is, the GM would have to come up with how the murder was done, what clues exist, who they point to, and why the antagonist killed the king. Their desire to seize the throne leads to more questions about why and what they will do if they achieve their ambition.

An interesting series of adventures could be built around an assassin who successfully blames someone else for the deed. If the evidence of the murder only surfaces after the murderer is crowned, do the player characters risk plunging the land into civil war to overthrow the usurper?

The murderer may not even have had evil motives: Suppose that the doddering, aged king refused to pass the reins of power to his eminently qualified successor, instead trying to manipulate the system to put a favorite (but unqualified) princeling onto the throne after he steps down. The murderer could have thought (rightly or wrongly) that the king's death would save the land from endless suffering and chaos.