Well, I was just wondering what is the catch rate of a Poke Ball that shakes in midair. I know that is isn't a perfect chance to catch when a Poke Ball shakes so what is the catch rate?

That is called a Critical Capture, and similar to a Critical Hit, it has a 10% Chance of occurring.

http://bulbapedia.bulbagarden.net/wiki/Catch_rate

Here is the quote:

The probability of a critical capture depends of the number of Pokémon that has previously been caught in the Pokédex. First, compute the value of a (the modified catch rate), as above. Then, whether or not this value is less than 255 (above which the Pokémon is caught regardless of whether or not it is a critical capture), multiply this value by the following: Species Caught Multiplier >600 2.5 451-600 2 301-450 1.5 151-300 1 31-150 0.5 30 0 A random number is generated, and if it is less than the modified value, a critical capture occurs.