In isomerization dynamics of Ar-7-like molecules of high energy, which is in the so-called liquidlike phase, a peculiar characteristic has been observed [K. Takatsuka and C. Seko, J. Chem. Phys. 105, 10356 (1996)], that is, the occurrence of a given geometric isomerization in a short Lifetime is less frequent than expected by an exponential distribution based on the mixing in dynamics. This behavior is exactly the reverse to those observed in the simpler system such as dissociation reaction of H-3(+) [M. Berblinger and C. Schlier, J. Chem. Phys. 101, 4750 (1994)], in which many of the so-called direct paths are ejected before the mixing takes effect and thereby the short lifetime isomerization (or dissociation) occurs more frequently than the exponential distribution. The former fact implies that the classical trajectories take somewhat longer time (induction time) to find their ways out to the other isomers in phase space, and therefore it can be a prototype of the so-called slow dynamics that is frequently observed in large and complicated molecular systems. The present paper discusses a possible mechanism to describe the present induction phenomenon. We first show a numerical fact that an ensemble of trajectories turns into a stage very quickly that can be regarded as a diffusion process getting out of a potential basin, if projected onto a one-dimensional configuration space. Thus, a natural idea arises that the induction time should be a consequence for the group of trajectories to be transported to the reaction regions, or transition regions, with a limited speed. In contrast, the standard statistical theories assume that the population in a transition region that is lost to the product side is to be supplied instantaneously from the reactant region. We present a simple diffusion model to examine the above idea. It has been found that the frequencies of isomerization can be reproduced in a good quantitative level by the estimate in terms of the first passage time based on the calculated diffusion coefficients and related quantities. The remarkable uniformity of the average passage-times (lifetimes) that was previously found by us is also described well in this simple model.