Another reason for the priors not being mentioned at trial may be that there is no need to do so. Some evidence setting the scene, background evidence, is likely to have been given as part of the narrative. For example, if a crime was committed by a person in a building, video surveillance evidence may be that only 10 people were in the building around the relevant time, including the defendant. This supports priors of P'(G) / P'(NG) = 0.1 / 0.9 = 0.11. Another example is where it is conceded by the prosecutor that only one of two people could have committed the crime, the defendant being one. It would be intuitive to think that this gave equal priors of P(G) = P(NG) = 0.5. But the prior likelihood of each suspect being the offender may not be equal, and the question becomes to what extent should the fact-finder be given evidence of the unevenness of the respective prior likelihoods.
The point is that to make presuppositions about the defendant's guilt or innocence legitimate, those probabilities must be assessed from evidence given at trial.