Probability and Sherlock Holmes

I was always concerned on how Sir Arthur Conan Doyle uses probability to justify Sherlock Holmes's evidence in indicting a certain suspect. He always assumes that the more the events there are to imply, the higher the probability for the whole scenario to happen. The truth is actually the opposite. The more uncertain events you're presenting to prove a point, the lower the probability that we get the right conclusion.

For example, if you saw a man with a dirt on his shoe. You could imply from this that the man didn't cleaned his shoe last night. You can imply from this that the man is probably tired last night and doesn't have the time to clean it up. You can imply from this again that he probably have gone to party last night, that's why he didn't get time to clean his shoes. It can go on and on until you land to a conclusion that the man has a dog in his house.

The problem arises when you put implication over another implications. Because you are never sure in every implication, the probability of the whole scenario that the man has a dog will be diminished. To address this problem you need to put another evidence to improve every level of implication. For example you know that it didn't rain morning of that day, then the event of him cleaning his shoe last night will be more probable to happen. Doyle uses this most the time. He puts more evidences in every level of Sherlock's implication. Still, we are uncertain in every conjecture that we devise, no matter what happen, the conclusion that we get that the man has a dog in his house will be more uncertain to happen. It is not the other way around that if we deal with more implications, the higher the certainty for the conclusion to be true, even if you could see that the whole story fits.