What is the relationship between people believing a claim and its veracity?

When asked to properly evaluate the likelihood of the Loch Ness monster one really can agree that it doesn't exist, but if you put the likelihood at actual zero rather than a number infinitesimally close thereto, you are being a bad skeptic.

If people state things as true and they are true 60% of the time, then we are correct to say there's a positive correlation there. Even according them a very wide wrong margin of 40% (especially considering things they assert are stuff like their names, whether they have pets, how they are doing, where such and such a person is). I am giving a very very wide margin of error, and even given a true/false set of facts guessing could only ever be 50%.

It holds accurate that people tend to be right more often than you would be right, if you were pulling answers at random. Especially in science where refinement and self-checking really gets the answers well into at least the 90%s of being correct.

I'm not looking at the world in rose colored glasses. I'm a skeptic, I do my best to see the world as it actually is. I think that "trust but verify" is a fantastic methodology for having the most true beliefs and the fewest false beliefs. That one can create a robust and functional epistemology. I am not saying, everything people say is true. I'm saying since things people say are more likely to be true than false, it holds that there is a positive correlation between what people believe and what are true facts about the world.

"How does the number of believers have any bearing on the veracity of the claim?"

And the answer is by being positively correlated. There's a number of good and proper responses to the supposing God exists because theists exists. Most people tend to believe in mutually exclusive gods. If everybody believed in unicorns but everybody disagreed as to what color all of them were, it would not what we'd expect of a true belief. Generally people believe in the sun exists, but there's very little disagreement as to what color it appears to be. Equally there are not demonstrated gods. Most people seem to believe chairs exists, and claim that chairs exists. When asked how they know, they will quite often point to a chair. With regard to gods they seem to insist it's impossible to demonstrate, which is an unusually characteristic for things that actually exist.

When I say I have a pet gecko, you would be correct to accept my claim tentatively. When I say I have a pet dragon, you would error to accept my claim, even tentatively. If I said that by "dragon" I mean komodo dragon, my claim becomes astronomically more reasonable, but you would still error to tentatively accept my claim as they are rare, endangered, illegal to own, and highly dangerous.

When you say you have a friend named Bob, and he's a dietitian, that would be a perfectly reasonable claim. When you say you have a friend named Bob, and he's a deity whose created the universe and is magically undetectable, everybody's bullshit detector should go off. The fact that the majority of people think this is true, does very little to dilute the absurdity of notion.

While it the better than average chance that what people say is true suffices to establish that what people tend to think tends (better than random) to be true, that meager amount of evidence is resoundingly rendered moot when you say things as absurd as religion.

If somebody tells you they are a Christian, they are generally going to be telling the truth, and you would do well to believe them. If somebody tells you that Christianity is true, you would do well to not.

Because the saying of things is good enough for trivial claims, but if you want to convince somebody that the creator of the entire universe donned a baby suit so that he could sacrifice Himself to Himself to give Himself permission to forgive His creation for their ancestors sins of eating magical fruit on the advice of a talking reptile, by utilizing His blood in some fashion to create a loophole in His own system, and through His perfect justice damn Mahatma Gandhi to eternal hell-fire for the evil of not believing this claptrap. You need more than words.

Saying something is true is evidence. And for minor claims it's often sufficient evidence for a claim. The problem here is that a billion people believing a lie cannot render it true. There are vastly more cases of a billion people being wrong about something than there are of some religion's creation myth being true, and their deities being real, or for magic.

What is the relationship between a great many people believing a claim and the veracity of that claim. The answer is they share a positive correlation (which means it's evidence). If asked whether that suffices to justify even one miracle, the answer is definitively no.