The Party is hired by the King to fake his murder and help him to escape his responsibilities. He will payout a massive reward for a job well done.
All this unbeknownst to the Queen, she also contacts the party to hire them to actually murder her husband the King. She will pay them well if they make it look like an accident.
Does the party help the king? Queen? Double cross? Double dip? Regardless, afterwards Lt. Columbo arrives on the scene with a clue.