A theoretical question on probe resistances for a voltage measuring device
@Lelesquiz has given you an answer that is applicable to low frequency changes in the signal, however to answer the question about current you really need to know the bias current of the amplifier, which (when modeled) appears as a constant current source at the ideal amplifier input. 

The bias current can be much larger than the input voltage divided by the input resistance. For example a precision op-amp such as an LT1013 might have an input bias current of 30nA but an input resistance of several G ohms. That will cause an error 30nA in the reading, even at 0mA from the transducer, which might be significant (or not).