If I understand the question, then you are asking 'Given a starting population of 10 000 individuals and 2 500 generations, what is the probability that one of the 5 000 000 000 individuals descendend individuals is directly descended from one of the founders?'.
If we are assuming no migration in or out of the system, then the answer must be 1, since there are no ways to be descended from someone outside the system. Please let me know if I have misunderstood the question.
For this, it's only possible to use uni-parental markers. This is because inferring exact genealogical relationships using autosomal markers beyond something like 3rd cousins is extremely difficult, owing to the stochastic way in which recombination breaks up segments. Beyond a few generations, only the uniparentally inherited mtDNA and non-recombining Y-chromosome can be informative about relatedness.
Uniparental markers don't recombine, so mutations aside, you expect to inherit an exact copy of your mothers mtDNA marker. If you know the number of generations which are likely to separate you and the putative ancestor, you can estimate the some kind of likelihood of being directly descended from the ancestor given the number of pairwise differences between the individual and the ancestor.
This is what they did when they wanted to identify the remains of Richard III. It's a good paper and easy to read / open access, so I'd recommend checking it out.
Simply, no. The inference of being a direct descendent from one of the ancestors would be independent from any of the other potential descendants in the sample.