The transition probability between the hyperfine splitting components of a hydrogenlike ion is expressed in terms of the bound-electron g-factor. It allows a simple calculation of the QED (quantum electrodynamic) and nuclear-size corrections to the transition probability by using the corresponding corrections to the bound-electron g-factor. In experimentally interesting cases of Ho, Re, Pb, and Bi the QED corrections increase the transition probability by about 0.3%. Using a recent experimental value for the transition probability between the hyperfine structure components in ²⁰⁷pb⁸¹⁺ it is found that the bound-electron g-factor in lead amounts to 1.78(12). The corresponding theoretical value is 1.7383.