Atmospheric reentry remains a critical phase in spacecraft missions due to the severe thermal loads generated by strong shocks and gas–surface interactions. Ground-based testing in plasma wind tunnels, such as the von Karman Institute for Fluid Dynamics (VKI) Plasmatron, plays a key role in replicating and studying these conditions. However, reliable heat flux predictions require accurate modeling of gas-surface interaction phenomena, particularly catalytic surface recombination. This study presents a probabilistic framework to calibrate the catalytic efficiency of the VKI standard probe, a reference copper surface, under varying pressure conditions. A surrogate model based on Gaussian Process Regression was trained on over 1200 simulations performed with the STAGLINE solver, an in-house one-dimensional CFD solver specifically developed to enable efficient computation of high-enthalpy, chemically reacting plasmas along the stagnation line. This model was then integrated into a Bayesian inversion framework using Markov Chain Monte Carlo sampling to infer catalytic coefficients for atomic nitrogen and oxygen. The calibration was constrained using experimental data from a dedicated Plasmatron test campaign, including wall heat-flux and free-stream temperature measurements. This represents an improvement in the calibration of catalytic efficiency, as the free-stream temperature is now used as an experimental input rather than being treated as an inferred variable in previous calibration approaches. This approach significantly outperform traditional catalytic coefficients reference models, reducing the prediction error by up to a factor of three in terms of Mean Absolute Error. The Bayesian framework demonstrates robustness across a broad pressure range and enables the definition of a new set of pressure-dependent catalytic coefficients inferred from experimental observations. These values offer a practical and data-driven alternative for reconstructing heat fluxes in ground-to-flight extrapolation methodologies.