 Consider again a stylized DNA evidence case. Suppose the prosecutor puts forward the hypothesis that the suspect left the traces found at the crime scene. This hypothesis is well supported by laboratory analyses showing that the defendant genetically matches the traces. The defense, however, responds by putting forward the following ad hoc hypothesis: “The crime stain was left by some unknown person who happened to have the same genotype as the suspect”. Since the probability of the DNA match given either hypothesis is 1, the likelihood ratio equals 1 (Evett, Jackson, and Lambert 2000). The problem generalizes. For any item of evidence and any given prosecutor’s hypothesis \(H\), there is an ad hoc competing hypothesis \(H^*\) such that