Femtosecond pump-probe experiments on the potassium dimer are simulated by quantum dynamical calculations and compared with the experimentally found results. At moderate laser intensities three neutral electronic states dominantly participate in the ionization process. The transition mechanism is a pure (1 + 2)-photon pump-probe process. The two-photon ionization process is located at the outer turning point of the wave packet in the A(1) Sigma(u)(+) state of the K-2 molecule. Both the favorable spectroscopic properties and the special molecular dynamics induced by the moderate laser intensities combine to open a Franck-Condon window for ionization via the 2(1) Pi(g), state which allows the selective detection of the vibrations in the A(1) Sigma(u)(+) state.