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The proximity-induced superconducting state in the three-dimensional topological insulator HgTe has been studied using electronic transport of a normal metal-superconducting point contact as a spectroscopic tool (Andreev point-contact spectroscopy). By analyzing the conductance as a function of voltage for various temperatures, magnetic fields, and gate voltages, we find evidence, in equilibrium, for an induced order parameter in HgTe of 70 µeV and a niobium order parameter of 1.1 meV. To understand the full conductance curve as a function of applied voltage we suggest a non-equilibrium-driven transformation of the quantum transport process where the relevant scattering region and equilibrium reservoirs change with voltage. This change implies that the spectroscopy probes the superconducting correlations at different positions in the sample, depending on the bias voltage.