A non-Jewish court conviction has no validity in Halacha and the Yid remains as innocent in the eyes of the Torah as he was before he was accused.
Aside from the standards of acceptable proofs of evidence being much lower in non-Jewish courts than in halachic courts, oftentimes what the accusations entail aren’t even crimes under Halacha.
And that’s before even getting into the point of taking 12 people off the street, who can easily constitute drunkards, homeless, unemployeds, people rushing to get done with the case paying them $45/day while they’re losing their salary, to decide the guilt of the accused. And prosecutors and judges looking to convict not because of actual guilt but so that the DA or judge can get re-elected and enhance their political career as being tough on crime.