A Permittivity Probe (PP) instrument is now on board the Philae lander of the ROSETTA mission, en route towards comet Churyumov-Gerasimenko. The objective is to deduce the complex permittivity of the comet after touchdown from mutual impedance measurements between two pairs of transmitting and receiving electrodes. The full set of electrodes, also taking advantage of the instruments APX and MUPUS, will be deployed only some time after landing and then nominal operations will start. However, considering all other elements including the lander body as extra electrodes, it is possible to derive the complex permittivity from early measurements when only the landing feet would be deployed. The geometry is less suited due to symmetry constraints but in-flight calibration of the reduced system can be performed before landing in this configuration. A numerical model of the instrument on Philae has been developed for simulating both free flight calibrations and first measurements on the comet. We discuss the results with respect to different crude models of cometary material.