They don't need a terribly high standard of evidence. They need enough circumstantial evidence (not proof) to tip the balance of probability. It's akin to 'given the evidence, would the average person believe City or the PL?'. Evidence in this case is the presentation of material that could be interpreted in ways that suggest City's guilt (or not). No smoking gun is necessary.
All of that said, it's not 51 vs 49. The evidence should be reasonably convincing.
I don't think the PL need or expect to win every argument, just enough to demonstrate City broke enough rules (deliberately) to be made an example of and appease a number of other PL members whilst being seen to be keeping their house in order.
If you will remember, the announcement of the 125 charges came in the face of the government turning its gaze on the effectiveness of the PL and the PL needed to demonstrate it could regulate itself... swiftly followed by similar action towards a few other clubs too.
The case is riddled with sporting and political agenda.