The part of this paper that is really interesting to me is § 8.3 Use of Databases in which they outline how to treat the database itself — the allele reference sample from the population — as part of the evidence.
Consider, for example, a simple model for a homogeneous population, with the (χ_{i}) initially exchangable, having de Finetti representation ... with β(a, b) prior:
dF(p) ∝ p^{a-1} (1-p)^{b-1}dp.
The symbol ∝ means proportional to. Suppose that the database δ is of size n, containing r instances of [the crime scene type]. There is also the finding on the suspect [having the crime scene type] so ...
[matching probability]=(r+1+a)/(n+1+a+b) .
For small a and b, this is approximately equivalent to adding the suspect to the database and using (approximately) relative frequency estimates. For large r and n, the effect of conditioning on the suspect becomes unimportant.
β(p;a,b) ∝ p^{a−1}(1−p)^{b−1}
In 1999 I presented the combination of this with Dawid & Mortera's formula above as a tenative solution to the matching probability for a rare haplotype. Assuming the haplotype occurs r=0 times in the database, the matching probability for an innocent suspect is 1/(n+1+θ). There are various ways to estimate θ, such as one less than the reciprocal of the empirical pairwise matching rate (hence θ≈9000 for US Caucasians). However while the idea (of adopting a β prior based on Ewens' result) is elegant I couldn't validate the result (because of the ideal assumptions) so chose not to recommend it in publication for actual court use.
Actually, for STRs it makes some kind of sense to take θ+1≈5, suggesting a matching probability of (k+1)/(n+5). However, note that typically k≈n/10 so ±4 in the denominator is as insignificant as ±½ in the numerator.