Clue is a board game in which you must deduce three details surrounding a murder. In the original game of Clue, the guilty person can be chosen from 66 people, and there are 66 different possible weapons and 99 possible rooms. At one point in the game, you have narrowed the possibilities down to 33 people, 55 weapons, and 44 rooms. What is the probability of making a random guess of the guilty person, murder weapon, and location from your narrowed-down choices, and the guess being correct? Enter a fraction or round your answer to 44 decimal places, if necessary.

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