We construct a combinatorially exact probability distribution for the problem of a priori clone overlap assessment in DNA fingerprint mapping. It is implemented as a general enumeration methodology using Bell's exponential polynomials. Established computational metrics do not consider the conditional nature of the problem. They dramatically overpredict actual match probabilities as a consequence. This elevates the rate of false-negative overlap declarations, which is consistent with previous validation studies. Increased measurement resolution does not significantly improve accuracy. We describe general trends in error behavior for intermediate-size DNA clones and discuss corresponding limits on the ability to assess certain overlaps.