The wave function can't be a probability (or probability density) since it's complex. A probability must obviously be a real number between 0 and 1.
Also, you you only start by taking the Fourier transform if you're interested in the probability density of a certain value of the momentum. If you're interested in the probability density of a certain value of the position, you don't have to do a Fourier transform.
As Fredrick said, you don't take Fourier transform of a wave function in the process of finding the probability density. The probability density is given by (in one dimension):
[tex]P(x)=\int\psi (x)^*\psi (x) dx[/tex]
which does not involve a Fourier Transform.
Instead, the Fourier transform of a wave function will give the wave function in momentum space (call it [itex]\phi[/itex]). Again, as Fredrick mentioned, we can use this to find the probability density for the momentum of the particle: