A card from a pack of 52 playing cards is lost. From the remaining cards  of the pack three cards are drawn at random (without replacement) and are found to be all spades. Find the probability of the lost card being a spade.

Explanation

To solve the problem, we need to find the probability that the lost card is a spade given that three cards drawn from the remaining cards are all spades. We can use Bayes' theorem to find this probability.

### Step 1: Define Events
Let:
- \( A \): The event that the lost card is a spade.
- \( B \): The event that three cards drawn are all spades.

### Step 2: Find Required Probabilities
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