A bag contains 10 balls out of which \(k\) are red and \((10-k)\) are black, where \(0 \leq k \leq 10\). If three balls …

A bag contains 10 balls out of which \(k\) are red and \((10-k)\) are black, where \(0 \leq k \leq 10\). If three balls are drawn at random without replacement and all of them are found to be black, then the probability that the bag contains 1 red and 9 black balls is: