To solve for \( P(\text{brown} | \text{black}) \), we want to find the conditional probability of selecting a brown pair of shoes given that we have selected a black pair of shoes.
According to the definition of conditional probability:
\[ P(A | B) = \frac{P(A \cap B)}{P(B)} \]
In this case, let's define:
- Let \( A \) be the event of selecting a brown pair of shoes.
- Let \( B \) be the event of selecting a black pair of shoes.
Since brown shoes and black shoes are mutually exclusive (you cannot have a pair that is both brown and black), the intersection \( A \cap B \) is empty, meaning \( P(A \cap B) = 0 \). Therefore, the probability \( P(brown | black) \) is:
\[ P(brown | black) = \frac{0}{P(black)} = 0 \]
In a more direct interpretation:
- The number of brown pairs is 26.
- The number of black pairs is 47.
- The total number of pairs is 100.
Since there are no pairs that are both brown and black, \( P(brown | black) = 0 \).
However, if we are asked how to calculate \( P(\text{brown} | \text{black}) \) in a way that does not assume they are mutually exclusive and instead consider probabilities within the context of pairs selected, the correct response should indicate the conditionality based on a total number of pairs.
But given the context of the question and the definitions, the most accurate and straightforward response remains:
\[ \boxed{0} \]