It’s really not that far of a stretch, the queen and her party moved to usurp the throne instantly and even locked up the kings sister breaking all norms only days after they tried and failed to move against the princess and the king came out reinforcing his support of his daughter even though he was incredibly sick.
The kings poor conduction only makes it more likely that they would kill him to get what they want as no one would question the case of his dead and even while sick he was in there way.