3 things.
Dd was pushing a very little cousin on a swing, when she started talking very matter-of-factly about her daddy being very ANGRY! and the house burning down. Since the little one's daddy is an extremely easygoing type dd couldn't understand the ANGRY! bit and said 'I don't think your daddy's ever angry, is he?'
'Oh, not THAT daddy,' she said, quite matter of fact. 'I mean my OTHER daddy, before.'
When I was about 12 my mother woke up one morning convinced that her sister thousands of miles away had had a baby. We all pooh poohed it - she'd surely have let us know she was pregnant?
But my mother was convinced and quite specific. She had woken at 6.30, looked at the clock and gone back to sleep until the alarm went at 7. In that time she'd had this very vivid dream about her sister - should add that they weren't even very close.
Anyway, we forgot all about it - until about 3 weeks later (this was long before email and when people didn't make long distance calls except in dire emergencies) when a baby announcement card arrived, with time and date. When we worked out the time difference, the baby had been born during that exact half hour when my mother had her dream. My aunt hadn't told us she was pregnant because she'd had two miscarriages before.
My mother was a hyper-sensitive type - which could make her difficult at times, very quick to get upset or take offence etc., - and I knew of at least one other incident where she knew exact details of a family member's distress thousands of miles away. In that case it was me, and she wrote to me (again, long before anything like email) terribly worried because she'd had a dream - and in the letter she gave exact details of what I had been planning to do. The letter in itself was very unusual - she never wrote, my father did.
Again, the date of the letter showed that she'd had the dream on the same night I'd been so terribly upset.
To be frank, although I knew she had 'form', it really spooked me and I never told her she'd been spot on.
It rather amuses me when people say they'd never believe in telepathy unless it was proved under lab conditions. Well, I know 100% that it exists, but in my mother's case it only happened a very few times that I know of, and only at times of great stress/distress in someone else. So I doubt she'd ever have been able to do it under lab conditions.
People often say, Oh, it must have been coincidence, but these were far too accurate to be that. Or they say, Oh, it's easy to 'know' after the event, but in these rare cases she always 'knew' , and said so, before she could possibly have known, IYSWIM.
In fact I don't think it's really so inexplicable, when you think how incredibly complex the human brain is. You can buy a very cheap and relatively simple radio that will pick up invisible waves - I think some people's brains can pick up thought waves, and I expect one day we'll understand how it works.