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That depends on the mutations, doesn't it?

Presumably, your postulate stands. However, for the sake of calculations, one must have some dividing line. Without such, there is no way to evaluate the probabilities.

The key point is that after thousands of generations, numerous mutations have been favorably selected, and have spread through the population. Others have been de-selected (by early death or reproductive failure) and have been removed from the population.

By observation, there are species currently in existence that are nominally evolutionary “precursors” of those that came at later times ostensibly as a result of the accumulation of enough mutations in the “gene pool” to have created these new species. By these observations, on can conclude that one of the “gene pools” did not accumulate mutations and another did. Therefore, to calculate the likelihood of enough favorable mutations having occurred in an alternate “gene pool” to qualify as a new species, there must be a definition of the number of mutations

Therefore, to calculate the likelihood of enough favorable mutations having occurred in an alternate “gene pool” to qualify as a new species, there must be a definition of the number of mutations

You're trying to invent your own definition of a new species, based on mutation count. All that's really necessary is that the two populations don't breed together. It could be something as simple as females of each group going into heat at different times. Or the populations may have developed slightly different coloration that causes each group to select for that, and to ignore the others. Or a slightly different scent. Speciation can result from trivial changes. At first. Over time, the separate populations will increasingly diverge. One group may remain relatively stable, as you remarked earlier. That can happen in a stable environment where there's little selection pressure.

Others are supplying you useful information about why your mental model of evolution is wrong but here's another: a species designation is not absolute, uniform, or subject to mathematical exactitude. In fact, most closely related, and soemtimes even far-removed, species can crossbreed at the gamete level and only after some significant embryonic growth is the developing organism subject to a life-threatening error, usually leading to miscarriage.