I was living in taiwan once - I had been there for several months when this happened. One morning, while studying, I turned to my roommate and, said "I think my sister is getting engaged."
What's weird is I have no idea why I spoke at all, much less why I said this exact phrase. I hadn't intended to speak to him, we were both busy with our studies.
Politely he said "What makes you say that?"
I said, "I... don't know why I said that." As far as I knew my sister had recently broken up with a guy who was terrible and wasn't seeing anybody.
Well a few days later I check my email and there's a message from my mom saying, sure enough, sis had gotten engaged. A little digging and I discover she had gotten engaged on that exact day, at that exact time, half a world away. Somehow I had known.