Can Ohmic contact in quantum Hall systems be considered a voltage probe?

Ohmic contacts are crucial elements of mesoscopic systems, which have no clear theoretical description yet. We propose a model of the Ohmic contact with a finite capacitance $C$ attached to a quantum Hall edge channel. It is shown that in contrast to na\"ive expectations the fluctuations of currents originating at such contact have non-equilibrium statistics. Consequently, the Ohmic contact can be considered a ``voltage probe'' only for certain values of the system parameters. In particular, the distribution function of outgoing electrons is close to the equilibrium one if the contact's temperature is much larger than $e^2/2\pi C$.