"In daily life, we don't demand logical certainly. We believe certain things, and act accordingly, based on a combination of logic, observation, and intuition.
For example, I just sat down on a chair. I assumed, justifiably, that the chair was secure enough to hold my weight. Although I would openly admit that from a purely logical perspective I had no good reason to believe that the chair would support, I maintain it was a perfectly reasonable assumption. It is unfair (and intellectually dishonest) to demand a higher level of evidence than the one we rely on so casually everyday."
Extraordinary claims need extraordinary evidence.
"On what ground do you make that distinction?"
You see chairs every day. You sit in them all the time. They almost always support you. It doesn't conflict with anything you regularly know about the world to assume this one will support you as well. It looks like it will and that's all the ordinary evidence you need for such an ordinary belief.
For claims that we know are possible, you need less evidence because all you need to prove is that it happened at a certain time and place. Claim: "There's an Asian elephant in the Bronx Zoo." Very possible, very believable. Show me a recent advertisement of that and I have no real reason to doubt it.
Other claims we may know to be possible, but highly unlikely. Claim: "Man was hit with lightning seven times in life." Pretty amazing. But I'm skeptical of his story since the odds of it are so low, though I admit it possible. Some paperwork, either reliable newspaper clippings, or maybe medical notes, or whatever documenting most of those hits would be enough for me.
And then still there are other claims which we don't think are possible, but hey, you never know. Claim: "The mansion down the block is haunted." Wow, haunted, that's incredible. I've never even seen a ghost or seen any reliable documentation of ghost sightings ever. Are ghosts even real? For this one claim, they claimant not only needs to prove that it is possible but that it did indeed happen.
And still there are claims for which sound completely absurd and for which we'd need a ton of evidence to support. Claim: "George Washington jumps over the Moon." I would need overwhelming evidence to support belief in that because the statement contradicts so much of what I already know about the world.
The claim of the theistic God fits somewhere along the lines of the haunted mansion claim and is far removed from the "this chair will support my weight" claim. Do you see the differences?