A comprehensive set of transition probabilities and radiative lifetimes of Rydberg states of alkali atoms (for Na, K, Cs, n<or=30; and for Rb, n<or=50) is obtained by using a simple, exactly solvable potential model for atoms. The results agree well with the available experimental values and other theoretical ones. Scaling relations for evaluating transition probabilities and lifetimes of high Rydberg states are also discussed. The well known (n*)^-5 scaling law of the transition probabilities A_{n(inf) not=n(inf)}/ with n' approximately=n>>1 is generally valid; however, the authors also find deviations from this law for some d to p and f to d transitions for Rb. A third-power polynomial is found to be better than the currently used exponential scaling law in predicting the lifetimes of even higher excited states.