  $\alpha$-decay always has enormous impetuses to the development of physics
and chemistry, in particular due to its indispensable role in the research of
new elements. Although it has been observed in laboratories for more than a
century, it remains a difficult problem to calculate accurately the formation
probability $S_\alpha$ microscopically. To this end, we establish a new model,
i.e., multistep model, and the corresponding formation probability $S_\alpha$
values of some typical $\alpha$-emitters are calculated without adjustable
parameters. The experimental half-lives, in particular their irregular behavior
around a shell closure, are remarkably well reproduced by half-life laws
combined with these $S_\alpha$. In our strategy, the cluster formation is a
gradual process in heavy nuclei, different from the situation that cluster
pre-exists in light nuclei. The present study may pave the way to a fully
understanding of $\alpha$-decay from the perspective of nuclear structure.
