The probability of getting some head/tails sequence is near 1 (cuz it could land on it's edge). The probability of predicting said sequence beforehand is extremely low.
The probability of someone winning the lottery is X, where X = the % of the possible ticket combinations sold. The probability of you winning the lottery with a particular set of numbers is extremely low.
As far as we can tell, and with the exception of the Old Testament heros, the probability of someone living to be 500 years old is much lower than winning most lotteries or predicting a certain high number of coin flips, though I suppose a smart ass could devise some exceptions to either. We'd have to better define "vampire" to arrive on a probability for that bit.
A house being haunted by real ghosts is actually extremely probable, depending on the neighborhood.
This is the explanation closest to what I was thinking beforehand. The problem seems like one of the difference between {the difficulty of predicting an event} and {the likelihood of correctly reporting an observed event}. I think Dagon's argument about Map vs. Territory is a good one too.
Question for you, though... please define "ghost"? I have a feeling your definition is different than mine because I find events such as
...certain environmental factors like (low-level poisoning from radon, carbon monoxide, et al; certain acoustic effects; certai
Alice: "I just flipped a coin [large number] times. Here's the sequence I got:
(Alice presents her sequence.)
Bob: No, you didn't. The probability of having gotten that particular sequence is 1/2^[large number]. Which is basically impossible. I don't believe you.
Alice: But I had to get some sequence or other. You'd make the same claim regardless of what sequence I showed you.
Bob: True. But am I really supposed to believe you that a 1/2^[large number] event happened, just because you tell me it did, or because you showed me a video of it happening, or even if I watched it happen with my own eyes? My observations are always fallible, and if you make an event improbable enough, why shouldn't I be skeptical even if I think I observed it?
Alice: Someone usually wins the lottery. Should the person who finds out that their ticket had the winning numbers believe the opposite, because winning is so improbable?
Bob: What's the difference between finding out you've won the lottery and finding out that your neighbor is a 500 year old vampire, or that your house is haunted by real ghosts? All of these events are extremely improbable given what we know of the world.
Alice: There's improbable, and then there's impossible. 500 year old vampires and ghosts don't exist.
Bob: As far as you know. And I bet more people claim to have seen ghosts than have won more than 100 million dollars in the lottery.
Alice: I still think there's something wrong with your reasoning here.