  We determine the phase diagram of an Anderson impurity in contact with
superconducting and normal-state leads for arbitrary ratio of the gap $\Delta$
to the Kondo temperature $T_K$. We observe a considerable effect of even very
weak coupling to the normal lead that is usually considered as a non-perturbing
tunneling probe. The numerical renormalization group results are analyzed in
the context of relevant experimental scenarios such as parity crossing
(doublet-singlet) quantum phase transitions induced by a gap reduction as well
as novel Kondo features induced by the normal lead. We point out the important
role of finite temperatures and magnetic fields. Overall, we find a very rich
behavior of spectral functions with zero-bias anomalies which can emerge
irrespective of whether the ground state is a doublet or a singlet. Our
findings are pertinent to the tunnelling-spectroscopy experiments aiming at
detecting Majorana modes in nanowires.
