This isn’t a prosecution, and nobody is alleging a crime. This is a civil lawsuit.
In a civil lawsuit, the standard of evidence is much different. You do not have to “prove” things beyond a reasonable doubt like in a criminal trial. The jury is instructed to weigh the evidence like a balance, and whichever side has the best evidence wins. Even if it’s only a small difference that only slightly favors one side, they win.
That’s why it’s so important to have evidence that counters whatever the other side claims. You are bound to lose if your opponents are the only ones offering evidence on their side of the balance.