A man is stranded on an island and a genie presents three boxes, 23 white marbles, and 7 black marbles and instructs the man, "you can distribute the marbles however you want to, but you must use all of the marbles. Once you finish , you will choose a box at random. If the marble is white you will escape from this place."

Assuming the man distributes the marbles in his best interest, what is the probability that he escapes the island?