Probabilistic arguments for deterministic systems are standard practice. Search for Erdős and probabilistic methods to see several examples in combinatorics.
In computation theory many proofs have the tagline "...with probability 1", meaning the author enumerated all desired possibilities and showed their probabilities summed to one. Most people accept this as proof, although it is less preferred, in the way that proof by contradiction is less favored than direct proof.
In computation theory many proofs have the tagline "...with probability 1", meaning the author enumerated all desired possibilities and showed their probabilities summed to one. Most people accept this as proof, although it is less preferred, in the way that proof by contradiction is less favored than direct proof.