Just updating an old answer here
I completely forgot about updating this, so;
The chance is (1/32)^6, which is equal to 1/1073741824, or in index notation, 9.313225746 x 10^-10.
This, in full decimal form is 0.0000000009313225746.
Basically, I'd fancy your chances of getting struck by lightning to be higher than getting a perfectly IVed Pokemon in the wild. If you do, buddy, go enter the lottery.
How to calculate it
The formula used in this case is n^r, from the topic of Probability/Combinations and Permutations. In this case, 1/32 is representing the chance of getting a single perfect IV on the Pokemon, while by taking it to the power of 6 represents that fact you need to get that perfect IV 6 times.