Physicist: First, “normal” things don’t catch the eye. There’s a natural bias toward noticing the out-of-the-ordinary.
Also (mathematically speaking), although the chance of any one particular unlikely event is unlikely (because it’s unlikely), there are a very large number of unlikely events that could happen. It’s this huge number of possible events that forces the probabilities to favor the “unusual happenstance camp”. Feynman summed it up pretty well:
“You know, the most amazing thing happened to me tonight. I was coming here, on the way to the lecture, and I came in through the parking lot. And you won’t believe what happened. I saw a car with the license plate ARW 357. Can you imagine? Of all the millions of license plates in the state, what was the chance that I would see that particular one tonight? Amazing!”
Everyday you’re exposed to billions of Weird things (I’m defining “Weird” as 1 in a million) that could happen. Substantially less if you don’t leave the house. Substantially more if you live outside of Kansas (that’s right, Kansas). The probability that something extremely Weird happens around you in any given moment is 100%. For example; if you get change for any transaction, the probability that you get that particular set of coins (those exact coins) is much less than 1 in a million. However the probability that you’ll notice a Weird event is fairly small. Luckily, this is something you can control.
Say you notice N things everyday that have the potential to be Weird. Every piece of toast hiding the Virgin Mary™, every pair of snowflakes that might be identical, every bird that may drop gold doubloons on you, etc. Then the chance of noticing something Weird is . Which means that every time you look at about 700,000 things you’ll have a 50% chance of seeing something Weird (which isn’t that bad, can you see 1,000 things now?). If you restrict you attention only to “big” Weird things, then you’ll find yourself pretty disappointed, and it’s because there aren’t a lot of big things that happen day-to-day.
Now most people would consider 1 in a million a little strict, so if you keep your eyes open you’ll see Strange things almost continuously.
Also, consider this: “close calls” are substantially more likely than “hits”. For example; you’re 8 times more likely to hit the bull (50 points ring) on a dart board than you are to hit the bull’s eye. Unless you’re like crazy good, in which case: keep it to yourself.