Chaos theory describes the underlying patterns and deterministic laws of dynamical systems that were once thought to have completely random states of disorder and irregularities, but found to be completely deterministic but simply highly sensitive to initial conditions.
Such high sensitivity to initial conditions in the calculations which govern the system limit our ability to accurately make predictions beyond a certain precision. This is the reason why weather can not be currently forecasted very accurately beyond 10 days or so.
It may also be why quantum systems appear probabilistic. Quantum systems can currently be only described in the mathematical language of probability, but this does not mean that quantum phenomena must by extension be probabilistic in nature. They may just as well be completely deterministic but extremely sensitive to initial conditions.