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We describe an approach to the description of the time-development of theprocess of strong field ionization of atoms based on the calculation of thejoint probability of occurrence of two events, event B being finding atom inthe ionized state after the end of the laser pulse, event A being finding aparticular value of a given physical observable at a moment of time inside thelaser pulse duration. As an example of such an physical observable we considerlateral velocity component of the electron's velocity. Our approach allows usto study time-evolution of the lateral velocity distribution for the ionizedelectron during the interval of the laser pulse duration. We present results ofsuch a study for the cases of target atomic systems with short range Yukawa andCoulomb interactions.

Joint probability calculation of the lateral velocity distribution in strong field ionization process