In a fairy tale, the fairy grandmother has assured the queen that her yet unborn baby prince will not die until the following set of conditions is fulfilled.

A scroll shall be prepared, and on the day of the birth and every subsequent birthday, a letter of the Greek alphabet from Α to Ω inclusively, chosen at random with replacement, shall be entered on the scroll. On the day that all the 24 distinct letters from Α to Ω of the alphabet appears, the prince will die.

Determine the expectation of the prince's life in years.