High-entropy compounds, where multiple elements occupy a single crystallographic site in a highly disordered manner, challenge conventional understandings of electronic structures based on periodicity and well-defined band dispersion. Here, we report a detailed nuclear magnetic resonance study of the high-entropy superconductor $X_{0.6}{\mathrm{Pt}}_{0.4}\mathrm{Sb}$ ($X$ = Ru, Rh, Pd, Ir), revealing a spatially homogeneous electronic environment in the normal state, in stark contrast to its crystallographically disordered lattice. The superconducting state exhibits a small but solid Hebel-Slichter coherence peak followed by a significant decrease in the nuclear spin-lattice relaxation rate, providing compelling evidence for fully gapped $s$-wave pairing. Our findings not only deepen the understanding of superconductivity in highly disordered quantum materials but also open an alternative pathway for exploring superconducting states in entropy-stabilized systems.

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• Spin-orbit coupling
• Superconducting gap
• Disordered systems
• Superconductors
• Nuclear magnetic resonance