They must have produced sufficient evidence to convince a judge in a criminal court that the defendant was guilty beyond reasonable doubt.
The CPS has provisions in place to (hopefully) ensure evidence is gathered fairly and shared with defendants and their lawyers. The Post Office failed at this, so the defendants didn’t stand a chance.
Any prosecution (private or public, there's no difference) is legally obliged to share any information or evidence that may help the defence. The judgement summary makes it clear that they didn't disclose their knowledge of the issues with the Horizon system, despite the fact they were clearly known to Post Office Ltd (presumably these concerns were not shared with the prosecution, they'd have had to disclose it). In the majority of the cases, the Horizon data was the only evidence, and it was presented with absolute surety. Any hint they were issues with the reliability of the data would have been instant and reasonable cause for doubt. We
think they took some money isn't a strong case.
Regardless, it's hard to sit back and look at the sheer number of cases they were prosecuting and not think
hold on, something's off here. The worse thing is that they knew their evidence was shit, yet carried on anyway.