I can't tell you what the chances for a critical capture are, except that I read somewhere that it's "about the same as a critical hit." Based on what I've seen, that seems about right, but it's hardly exact.
What I can tell you, however, are the mechanics behind how captures work and how the mechanics of a critical capture work.
Essentially, there is some calculation that is performed 4 times. It can result in either a success or failure, which is depending on many factors, including the pokeball you used, the status condition of the pokemon you're targeting, its hp, capture rate, etc. For each success the calculation yields, the ball tilts one time. If all 4 succeed, then you catch the pokemon.
For a critical capture, the calculation is performed only once. If that one is a success, you capture the pokemon. If not, it escapes. It's that simple.
Disclaimer: I don't remember where I initially found this information.