There is a deck of 52 cards.
3 people each draw one card leaving 49 cards left in the deck.
The cards are hidden and known only to the person that drew the card.
Each person then says something about their card that gives a clue as to what it is.
A fourth person records all the clues and then the three cards are exposed.
After repeating this process a million times, the fourth person has the probability of what card each of the three people have based on their clue. The probability is derived from the frequency of them holding a specific card given the clue.
With the above conditions, what is the probability of drawing a given card from the deck after the three people have drawn their hidden card and given their clue?
For example:
Person 1 has (25% A$\spadesuit$, 25%, K$\diamondsuit$, 25% Q$\heartsuit$, 25% J$\clubsuit$, 0% rest of the cards)
Person 2 has (10% A$\spadesuit$, 30%, K$\diamondsuit$, 30% Q$\heartsuit$, 30% J$\clubsuit$, 0% rest of the cards)
Person 3 has (75% A$\spadesuit$, 5%, K$\diamondsuit$, 10% Q$\heartsuit$, 10% J$\clubsuit$, 0% rest of the cards)
What is the probability of drawing the A$\spadesuit$ from the deck given the high probability that it is no longer in the deck?
What is the probability of drawing the J$\clubsuit$?
What is the probability of drawing any of the rest of the cards?
Without the above conditions, the probability of drawing any given card is 1/52 since each card is equally likely of being drawn.
But now with the condition of what each person may hold I am unsure of how to solve for the probability of drawing the next card. If the A$\spadesuit$ has a low probability of being in the deck then there must be an increase in the probability of drawing any other card.
How exactly do you combine the players' probabilities of holding the A$\spadesuit$ with the probability of it still being in the deck and then how would that effect the drawing probability of all the other cards? Any help would be appreciated.