If you fire a single particle between two slits just once and it still forms a wave-like interference pattern, then surely what is being observed is more than just a probability distribution?
That's not a thing. There's no pattern to observe from a single particle.
The situation you're describing doesn't exist.
Wave behavior and interference patterns can only be observed in statistically significant collections of particle interactions. Not single interactions.
My point was that 1 sample in isolation won’t give you information about the underlying distribution, except that it’s non zero at that point, maybe?
Can you ever be sure you only fired a single particle?
“The atoms themselves are only ever observed in a given experimental run as particles – just as quantum mechanics says they should be. The wavelike behaviour – which is to say, the smeared-out probability distribution – is reconstructed from many particle-like observations.”