  We study formation and evolution of the electron wave-packets in the process
of strong field ionization of various atomic targets. Our study is based on
reformulating the problem in terms of conditional amplitudes, i.e., the
amplitudes describing outcomes of measurements of different observables
provided that the electron is found in the ionized state after the end of the
pulse. By choosing the electron coordinate as such an observable, we were able
to define unambiguously the notion of the ionized wave-packets and to study
their formation and spread. We show that the evolution of the ionized wave
packets obtained in this way follows closely the classical trajectories at the
initial stages of evolution providing an {\it ab initio} quantum-mechanical
confirmation of the basic premises of the Classical Monte Carlo Calculations
approach. At the later stages of evolution the picture becomes more complicated
due to the wave packets' spread and due to interference of wave packets
originating from different field maxima. Our approach also allowed us to obtain
information about the coordinate and velocity electron distributions at the
tunnel exit.
