Even some of the most adamant skeptics have survived experiences that cause them to believe in the possibility of ghosts, or a large ominous spiritual world.
In some cases these stories take the shape of a mysterious interaction with a person (or ghost figure), an inexplicable gut feeling, or some sort of psychic premonition. Other times, it's a run-in experienced by multiple people, a strange blip in time or the weather, or an unexplainable form of protection.
I was riding my bicycle down a narrow path. Maybe 30 meters in front of me was an elderly woman also on a bike. I was going fast and catching up to her quickly. I was a couple of meters from passing her when the path took a right turn and she was out of my sight for a second.
I should have been right behind her after I, too, had taken the right turn, so imagine my surprise when she had just...vanished. There was an open field to the left, a highly fenced off area (with no gates) to the right and one straight road ahead of us - no trace of her anywhere. I know the area well and there is no way she could have been hidden anywhere. This woman just went POOF and it puzzles me to this day.