To be a little more constructive: The probabilistic interpretation is odd, since it can only produce a few (maybe even one!) distinct values. $k$ should proba

To be a little more constructive: The probabilistic interpretation is odd, since it can only produce a few (maybe even one!) distinct values. $k$ should probably be chosen to avoid ties (e.g., odd for a two-class problem) so you always get exactly one answer, and you should definitely chose $k$ using different data than you use to evaluate the model (e.g., validation set or inside a cross-validation loop).