The King is Dead by Ellery Queen
'Ellery Queen IS the American detective story' Anthony Boucher.
King Bendigo is the wealthiest man alive. He has an enormous security detail on his private island, quite capable of dealing with international aggression. But not threats from within his own family. Fearing for his life, he hires brilliant detective Ellery Queen.
The King's brother Judah makes no secret of wanting him dead. He even gives a date and a time on which he will commit the crime. So when the day comes, the King is kept in a hermetically sealed room while his brother is guarded by Ellery himself.
But the King is still shot...
This is the ultimate in locked-door mysteries from a classic master of the genre.