Transfer function and voltage probes
The transfer function (unless there is a load on the output) is simpler than your equation because Z3 can be regarded as a short circuit between the top of Z2 and the output. In effect you have a potential divider formed by Z1 and Z2.

If you have a load then the TF is more complex because you have to take into account the potential divider formed by Z3 and the load AND the impedance this creates in parallel with Z2.

In all of this I am assuming the input feeds Z1 and the output is at Z3. 

So, the TF is simply \$\dfrac{Z_2}{Z_1+Z_2}\$ when the output is unloaded.