The King believes in fate and chance, kind of like the "luck of the draw." He does have absolute power because he creates the arena where he feels "poetic justice" will prevail. His justice system was to take the accused and put them in an arena and pick what is behind door number one or door number two, you live or you die. The King felt destiny/fate would decide whether one was guilty or innocent. If you are lucky, you live and marry a beautiful maiden and the King doesn't care if you are already married because he makes the rules and you have a new bride. If you are guilty, then fate has the criminal pick the door of death. The King wants to have the ultimate say in everything, " nothing pleased him so much as to make the crooked straight and crush down uneven places." The King doesn't want anything to happen that causes turmoil or upset so by setting up his arena, every criminal or innocent will have the same choice for their sentence with no one opposing his system of the law.
Reference: The Literature and Language Book by McDougal Littell
The king has complete power because he controls who is accused. Although the king contends that his "semi-barbaric method of justice" is perfectly fair, once someone is accused, he is in effect already punished. Of the two choices, of course, death is worse, but either way, the accused's life is forever changed. Guilt or innocence does not play a role here. The narrator indicates that the amphitheater, where the choice of two doors is made, "was an agent of poetic justice, in which crime was punished, or virtue rewarded, by the decrees of an impartial and incorruptible chance." All the king has to do is to accuse someone, and the king's problem is solved. He is "semi-barbaric" so the concept of a jury trial does not even exist. The king actually absolves himself of the responsibilty for the fate of the accused by using his method based on chance.