Wiktionary
adv. (label en probability theory) With probability equal to one.
Wikipedia
In probability theory, one says that an event happens almost surely (sometimes abbreviated as a.s.) if it happens with probability one. In other words, the set of possible exceptions may be non-empty, but it has probability zero. The concept is precisely the same as the concept of " almost everywhere" in measure theory. In probability experiments on a finite sample space there is no difference between almost surely and surely, but the distinction becomes important when the sample space is an infinite set (because an infinite set can have non-empty subsets of probability zero). Some examples of the use of this concept include the strong and uniform versions of the law of large numbers, and the continuity of the paths of Brownian motion.
The terms almost certainly (a.c.) and almost always (a.a.) are also used. Almost never describes the opposite of almost surely: an event that happens with probability zero happens almost never.
Usage examples of "almost surely".
To have detected the flotilla's emergence wave, the patrol ship had almost surely been on the near side of the system and outside the Oort Belt, which might have been coincidence, or .
The Macurdy men were well known for their strength, but Will was almost surely the strongest man in Washington County, and fast-moving.
Given Keltorus' hatred of the Sisterhood, she'd almost surely have been killed, brutally, if she'd continued alone to Ferny Cove.
He was looking for the key person in what seemed a major conspiracy, a person almost surely in some high or at least highly influential position.
The much-promoted Strategic Defence Initiative is a Cold War boondoggle, and SDI is almost surely not long for this world, in either budgets or rhetoric -- but both Navstar and spy satellites have very promising futures, in and/or out of the military.
Kadiya's talisman was almost surely lost to Portolanus, and Anigel's would very likely be given to the sorcerer in ransom before long.
Lovecraft of cancer of the esophagus, almost surely brought about by his curious diet, and perhaps the secret indulgence in certain fungi.
And Kaidu almost surely would be, if unopposed, for just now among the Buriat there was a ferment to unite under a strong khan.
We disagree: we might not, almost surely would not, get the same primate coming down from the trees, but equivalent major innovations would occur in the new and different lineages.
But in less than a hundred years we will almost surely hear from them.
He didn't see how he was going to eliminate anyone as the mastermind who'd almost surely done something to that Deputy Ida Weaver and been trying to do something to him ever since he'd talked to the deadly but not-too-bright little gal.