Weak measurements with arbitrary probe states

The exact conditions on valid probe states for weak measurements are derived. It is demonstrated that weak measurements can be performed with any probe state with vanishing probability current density. This condition is found both for weak measurements of noncommuting observables and for c-number observables. In addition, the interaction between object and probe must be sufficiently weak. Strange weak values can be observed also with mixed probe states, but not for c-number observables.