Cepheid-based determinations of the Hubble constant stand in significant tension with early-Universe inferences from the cosmic microwave background. While this tension is often discussed in terms of new physics or unmodelled systematics, the role of the assumed priors on the model parameters has received comparatively little attention. Recent work has pointed out that the commonly adopted flat prior on distance moduli upweights smaller distances and systematically favours high inferred values of the Hubble constant. Motivated by this observation, we perform a comprehensive Bayesian recalibration of the distance ladder, applying physically motivated priors uniformly to all distances, including the Milky Way Cepheids, which are incorporated directly into the joint fit. Together with a conservative treatment of the Gaia EDR3 residual parallax offset, the Hubble constant shifts from H₀ = 73.0±1.0 km s⁻¹ Mpc⁻¹ to ⁠H₀ = 70.6±1.0 km s⁻¹ Mpc⁻¹, reducing the Hubble tension from 5σ to 2σ⁠. Our results show that the assumed priors – often treated as innocuous defaults – can play a central role in the Hubble tension. Because all local distance ladders rely on the calibration of distances, similar prior-driven effects are expected to arise across distance-ladder methods.