in all probability

"If I am right in my own persuasion that such a document as I here describe is at this moment in Admiral Bartram's possession -- a persuasion based, in the first instance, on the extraordinary words that I have quoted to you; and, in the second instance, on purely legal considerations with which it is needless to incumber my letter -- if I am right in this opinion, the discovery of the Secret Trust would be, in all probability, a most important discovery to your interests.