This study presents a Bayesian probabilistic framework for predicting the bond strength of internally confined reinforced concrete beams, addressing the inherent limitations of conventional deterministic design models. Bond strength is formulated as a stochastic response by explicitly accounting for both epistemic uncertainty in model parameters and aleatory variability in material behaviour. Prior mechanical knowledge from established bond models is integrated with a large experimental database through Bayesian inference, enabling physically informed and data-consistent calibration. Posterior parameter distributions are estimated using Markov Chain Monte Carlo simulation with the Delayed Rejection Adaptive Metropolis algorithm, allowing efficient exploration of a high-dimensional and correlated parameter space. The proposed framework provides full predictive distributions of bond strength and associated credible intervals, rather than single-point estimates. Model calibration and validation are performed using a comprehensive experimental database comprising 273 reinforced concrete beam splice specimens reported in the literature. Validation results demonstrate strong predictive performance, with an RMSE of 0.89 and a coefficient of determination of R2=0.84, while approximately 95% of experimental observations fall within the 95% posterior credible intervals. The probabilistic model maintains physical transparency and parameter parsimony, while capturing key interactions among material properties, geometric parameters, and confinement effects. The proposed approach offers a robust and adaptable alternative to traditional code-based formulations, supporting risk-informed and performance-based design of reinforced concrete structures.