You just confirmed my point, you dont treat supernatural events in the same manner as natural events. You should check for the evidence for both events in an equal manner.
That would be true if it weren't for our background knowledge, which is part of the evidence. For instance, you need increasingly more and more evidence for the following scenarios.
- I walked to the store. You don't need any evidence that this sort of thing is possible.
- I drove my car to the store. Same here, although there might be some small question as to whether I have a car.
- I drove a tank to the store. You know that tanks exist, but you don't know that I'm the type of person that could have a tank, much less drive it to the store.
- I drove an interstellar spaceship to the store. You don't even know that this spaceship exists, much less that I have one, much less that I took it to the store.
All of those scenarios depend on background knowledge to help determine how much evidence would be needed to accept the claim. We have very poor evidence that anything supernatural is possible, so poor that we conclude - tentatively - that the supernatural is not possible.
***I see below that you say you have good evidence for the supernatural, so that's where the issue really lays, I think.