Published in Mike Resnick and M H Greenberg (eds) SHERLOCK HOLMES IN ORBIT

I'm afraid that this story, though cute, really strained my abilities to suspend disbelief. Not only are we expected to believe that Charles Babbage actually created a computer which became a state secret, but this computer was supposed to have been powerful enough to run an artificially intelligent program which was a sentient "Sherlock Holmes". The mention (but apparently, not much of an understanding) of the binomial theorem and its counterpart in probability theory are not enough to save this story in my mind.