You've decided to start training for the Iditarod, and a friend has gone out to get some puppies to form your sled dog team. She knows of two litters of puppies, one litter with short ears and one litter with floppy ears. Each litter has nine puppies, and she will bring home some number of puppies from each. There is an equal probability of her bringing back any number (from 0-9) of puppies from each litter. Given that your friend brought back k puppies, what is the probability that you have 5 short-eared puppies? Consider all values of k that lead to non-zero probabilities.