Transition probabilities per time unit in the spectrum of the hydrogen atom confined in a spherical cavity are studied with the Dirac equation. The calculations are performed with simple and accurate expansions of the Dirac components provided by the Lagrange-mesh method with small numbers of scaled Jacobi mesh points. The initial and final states as well as intermediate states occurring in two-photon transitions are described with a single Lagrange mesh. With this simplification, accurate matrix elements are easily computed with the Gauss quadrature associated with the Lagrange–Jacobi mesh. One-photon transitions are considered from the \(n = 2\) and 3 levels. Most transition probabilities increase as a negative power of the confinement radius when it becomes small. The two-photon \(2s_{1/2}-1s_{1/2}\) transition stops being the main deexcitation channel of the \(2s_{1/2}\) level when the confinement radius decreases below about 15 atomic units. The \(2p_{1/2}\) and \(2p_{3/2}\) levels come below the \(2s_{1/2}\) level and allow a faster one-photon deexcitation.