On Mount Olympus, Zeus is about to announce the name of the winner of the "Greatest Hero in Greek Mythology" award. The finalists are Theseus, Jason and Herakles. Theseus believes that he has a 25%...

On Mount Olympus, Zeus is about to announce the name of the winner of the "Greatest Hero in Greek Mythology" award. The finalists are Theseus, Jason and Herakles. Theseus believes that he has a 25% chance of winning and that Herakles is twice as likely to win as is Jason. To build suspense, Zeus is going to call out the names of the two finalists who didn't win before naming the winner, like this: "The second runner-up is X, the runner-up is Y, and the winner of the award is Z." Theseus believes that the announcer is equally likely to name either Jason or Herakles first if Theseus himself is to be named the winner. Then Theseus happens to overhear a conversation between Zeus and Aphrodite, and learns that Zeus will name Jason before Herakles ("Jason. Theseus, Herakles"). We will use p to denote the probability that Theseus assigns to his being the winner of the award. In what range does p lie after hearing this new information?