What was the balance of probability.

source: http://www.literature.org/authors/doyle-arthur-conan/sign-of-four/chapter-01.html

"This is unworthy of you, Holmes," I said. "I could not have believed that you would have descended to this. You have made inquiries into the history of my unhappy brother, and you now pretend to deduce this knowledge in some fanciful way. You cannot expect me to believe that you have read all this from his old watch! It is unkind and, to speak plainly, has a touch of charlatanism in it."
"My dear doctor," said he kindly, "pray accept my apolo- gies. Viewing the matter as an abstract problem, I had forgotten how personal and painful a thing it might be to you. I assure you, however, that I never even knew that you had a brother until you handed me the watch."
"Then how in the name of all that is wonderful did you get these facts? They are absolutely correct in every particular."
"Ah, that is good luck. I could only say what was the balance of probability. I did not at all expect to be so accurate."
"But it was not mere guesswork?"

My dictionary says:
(on) the balance of evidence/probability
(formal) (considering) the evidence on both sides of an argument, to find the most likely reason for or result of something

But I still don't understand the blue words, could you tell me what they mean?

Thank you.