I realise this isn’t quite the answer you’re looking for, but not really.
First of all, we should pigeonhole me. I tend to regard myself as an agnostic, but that’s slightly vague. I can imagine evidence that might convince me of religious/supernatural phenomena, but I can also believe that God/the universe has reasons to hide these. I don’t necessarily think we can’t know, but I think we might not be able to. And while I suspect I can be conveniently classified as a skeptic (I even had a subscription to Skeptical Inquirer for a period), I don’t self-identify as one. I find the dubious stuff too entertaining, I’m uncomfortable about too many aspects of organised skepticism (for a start, “skepticism” seems far too American a term - damn it, you’re sceptical), etc. I also like to delude myself that I’m too self-aware to be pigeonholed.
That said, what has happened on occasion is that I’ve had what you could call borderline paranormal experiences, that is experiences that, as they happened, were hard to explain and disconcerting. A good few classic UFO sightings that sometimes took some time to figure out or were momentarily very convincing, a ghost story that was scary while it was happening, … that sort of thing.
Of course, that I could explain such occurances has tended to make me more sceptical. They’ve also made me realise how important it is to be there if you want to figure out the explanation. In most cases, the experience was convincing because I couldn’t see or understand some detail. Bring that to your attention and you suddenly snap out of the illusion. And while it’s a cliche to dismiss anecdotal evidence in argument, this is why I personally dislike being asked to explain it. The account is likely to omit exactly the detail that’s crucial.
But my most interesting borderline experience is worth recounting because it is a case where I think the odds of coincidence can be usefully estimated. One Saturday afternoon in the early 90s, I had bought a copy of Walter S. Gibson’s Thames and Hudson book on Hieronymus Bosch. That evening I briefly flicked through it and came across a picture of Bosch’s Ascent of the Blessed from the set of panels in Venice. As the title suggests, this shows souls being lifted up to Heaven by angels. The striking thing is that the route there is a tunnel with a bright light at the end. And I though, hmm, that looks like reports of near-death experiences. Because I was due at a party, I had to put the book aside, but conciously made the mental note-to-self to have a closer look at the issue. Next morning, I walk into the common room in the student halls I was in at the time and, as usual in those days, start wading through all the British Sunday papers. And in the Sunday Telegraph I come across a full page article by someone who’d had the same thought on seeing the painting in the Palace of the Doges.
Now this was undeniably spooky. Particularly given the connection to NDEs. Or Bosch for that matter.
Yet, on reflection, I think that someone in the UK was sort-of likely going to have exactly that experience that morning. Why ? The book’s been in print a long time, the World of Art series is very popular and so is Bosch. So Thames and Hudson must be shifting at least one copy a week. Most of those are probably bought on Saturdays. So it doesn’t seem that improbable that someone was going to buy it that Saturday. And, since the resemblence is striking, I’d expect most buyers to hit upon the possible connection early on. The only question then is how likely are they to read the Sunday Telegraph. This is not a certainty; indeed I haven’t read a copy in perhaps the last ten years. Yet they’ll probably be a broadsheet reader, so that increases the odds there. Perhaps a 1-in-10 chance ? Overall, it seems to me that the odds of someone in the UK buying the book on the Saturday, realising the resemblence and then reading the article are probably somewhere in the 1-in-100 range. So what happened wasn’t probable (even allowing that it could happen to anyone and not just me), but it’s not startlingly unlikely.
For the record, Gibson has a plausible explanation for the layout that doesn’t involve Bosch having had a NDE. The issue actually seems to me, on reflection, interesting but not terribly important. Even if Bosch had such an experience, knowing he did wouldn’t tell us much, though it rules out a few of the explanations for them that have been proposed over the years.
Finally, something like utterly intuitive love-at-first sight is inexplicable when it happens to both of you. But that’s not something you even want to think about rationally.