To calculate \( P(\text{brown} | \text{black}) \), we need to find the probability of having a brown pair given that a black pair has been chosen.
Using the definition of conditional probability:
\[ P(\text{brown} | \text{black}) = \frac{P(\text{brown and black})}{P(\text{black})} \]
However, in this situation, since the pairs of shoes are separate and there are no overlapping pairs (i.e., no pair can be both brown and black at the same time), \( P(\text{brown and black}) = 0 \).
Thus, from a practical perspective, a pair can't simultaneously be brown and black. As there are 0 ways to pick a brown pair that is also black, the above expression simplifies to \( P(\text{brown | black}) = 0 \).
So the correct interpretation is that the probability \( P(\text{brown} | \text{black}) \) does not yield any of the options given due to there being no possibility of selecting a pair that is both brown and black.
Final answer:
\[ P(\text{brown} | \text{black}) = 0 \]