It's a good question. The interference pattern is a result of two things: 1) Quantum mechanics: the pilot wave or whatever you want to call it. 2) Incoming pa

It's a good question. The interference pattern is a result of two things: 1) Quantum mechanics: the pilot wave or whatever you want to call it. 2) Incoming particles' positions having a broad statistical distribution. With a cunningly skewed / rigged distribution you wouldn't see fringes (e.g. suppose they all come in on the same trajectory). However such distributions are atypical.* But we talk about probability being a 'measure of ignorance' here because we don't know where these particles are exactly, but we know they must have gone through the initial slit, and QM says: in that case, here's the probability it will end up at this final destination. * This the same story as statistical mechanics. (Having said that we do have the issue there that our systems start in low entropy, or 'atypical', states. That's a whole other topic)