One for the math nerds.

[Crusader]

If such a formula could be determined, would that mean that there would be a pattern to the madness of the entire 'There's only a probability that the particle is there' thing? If so, would that imply that we very well could be living in a 100% deterministic universe? (Divine intervention aside) Please pardon my ignorance on the subject.
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Sort of,things like the "Particle that is actually only a wave that has no particale in it" thing is a very complex matter. To explain through an 'easier' example: The speed of light is the fastest speed possible according to einstein's formulas. Light, therefore, cannot have a mass, because if it did, it would need infinite energy to accellerate to that point, thus light can have no mass whatsoever, but what is a particle without mass? Light can be proven to be a wave, however, but a wave of WHAT? What is moving in a wave? Welcome to the grand adventure of quantum mechanics, where many dimensions exist (we got 3d(length, width, depth)4d=time but these guys have at least 9 dimensions), where these questions are researched.

As for the "we cannot determine where an object is EXACTLY, but we can guess" thing (electron clouds, for instance), this is another of those big questions. The electron (cloud) is moving around the core of the atom. This is no pretty orbit like the moon around Earth, however, here the laws of nature concerning subatomic particles are at work. Human minds are breaking their heads over this stuff, because it's extremely alien to our mindset. Try Reading Hawking's work, by the time you are at page 25, where he starts about "negative particles" (antimatter, in a way) you totally lost his reasoning because of the complexity of the stuff (no light reading for someone with only high school maths and physics to build on).

However, this thing worked the other way around, from reading the energy levels in one particular type of atom, the sequence of primes could be derived, so this one went from quantum physics, to math, However, the prime numbers are extremely important, and by finding out a formula for them, maybe they can apply that formula the other way around again, apply it to atoms, and determine characteristics that have eluded us to this moment, if we start to better understand the subatomics and quantum physics working at this point, maybe we can come to a point where we can determine the place of electrons in a cloud with 100% accuracy, but such a thing is not dreamt of as possible for now.