Your question on the probability needs to take time into account. Assuming the neutral mutations are independent (e.g. must occur at different positions), that the long term frequency of the occurence of any combination would be the product of the long term frequencies of the individual mutations. OTOH the probability that such a combination will occur within G generations approaches 1 as G increases w/o limit (again assuming independence).
So does the concept of nonfunctional mutations get you anywhere?
Where were we trying to go? Selection can't grab hold of neutral mutations so they'll drift randomly with some long range tendency. They can get locked in by a positive change. The fact that they exist is meaningful in terms of the size of the genetic phase space. Anything else?
But that all is still missing the point. It's not generally interesting to talk about the likelihood of some spcific mutation or combination of mutations occuring. If I may be permitted my own analogy, suppose you are playing poker. You'd be silly to consider only the likelihood of a royal flush in spades; all combinations need to considered for a good analysis.
Continuing the analogy, you must consider process too. Among all the combinations of hands in draw poker, about half are a pair or better. With the draw however, the odds are very sigificantly increased so ignoring the draw (selection) would be a very bad error. Taking the point a bit further, an analysis of a poorly understood process doesn't make for a convincing argument.
If the set A of which we are trying to determine P(A) were so clearcut as the set of all five playing cards constituting a poker hand, we would not be having this discussion. I submit that we now know far too little to know what A is, even in sketch form. So the only thing we can "compute" (at least in concept) is the probability of one river crossing, to refer to my metaphor. Having some idea what that probability is (on average, under stipulated assumptions), we can reason backwards and determine what the size of A must be (or be like in orders of magnitude) for the evolutionary hypothesis to be true. I would adjust your poker analogy by saying that the poker hand the probability of which we are trying to get a fix on is also an unknown. In those circumstances, the best we could do is compute the probability of an unordered set of five playing cards, drawn without substitution, call it F, and say that P(A) equals #A * F.