Lucifer and Mamba are trying to construct a right-angled triangle. Lucifer chooses a positive real number randomly for the base and similarly, Mamba chooses a positive real number randomly for the perpendicular.

Given that the hypotenuse is smaller than $2003$, what is the probability of the absolute difference of the two chosen numbers being greater than $1$ ?

Print the greatest integer smaller than or equal to $(\text{answer} \times 10^8)$.