A general nonperturbative approach to calculate femtosecond pump-probe (PP) signals is proposed, which treats both the intramolecular couplings and the field-matter interaction (numerically) exactly. Experimentally as well as in a perturbative calculation it is straightforward to distinguish between different spectroscopic processes through the direction of the wave vector of the emitted radiation. A nonperturbative calculation, on the other hand, yields the overall polarization of the system, which is the sum of all these contributions. We present a general and practical method that allows to extract the individual spectroscopic signals, which are resolved in time, frequency, and direction of the emission, from the overall polarization. We briefly derive the basic expressions for the time- and frequency-resolved PP signals under consideration, and discuss in detail the simplifications that arise when the usual assumptions (i.e., weak laser fields, nonoverlapping pulses, slowly-varying envelope assumption and rotating-wave approximation) are invoked. The computational procedure is illustrated by nonperturbative calculations of the polarizations and PP signals for a one-dimensional shifted harmonic oscillator. To demonstrate the capability of the approach we have evaluated the polarization as well as PP signals for a three-dimensional model system with vibronically coupled potential-energy surfaces, which describes ultrafast nonadiabatic isomerization dynamics triggered by the twisting of a double bond. We consider various wavelengths and pulse durations of the laser fields and study integral and dispersed PP spectra as well as coherent photon-echo signals. It is shown that the time- and frequency-resolved PP signals reflect in real time the disappearance of the reactants and the delayed appearance of the products.