  It was proposed recently that the fine-grained entropy of the Hawking
radiation can be expressed by the semiclassical island formula, which
reproduces the unitary Page curve. In this paper, we choose the ``in'' vacuum
state and apply the quantum extremal surface construction to study the Page
curve for the step-function Vaidya model of evaporating black holes in four
dimensions, which is produced by the spherical null shells. Metrics of the
three regions of this spacetimes are obtained. In addition, the entanglement
islands for the step-function Vaidya model of evaporating black holes at very
late times are studied. When cutoff surface $A$ is located in Minkowski region
III with $u_A < u_H$ at very late times, we find that the location of the
boundary of island $\partial I$ depends on the value of $8M-v_A+v_I$.
Specifically, $\partial I$ is inside, at or outside the horizon when
$8M-v_A+v_I$ is less than, equal to or larger than zero respectively. Moreover,
when cutoff surface $A$ is located in Minkowski region III with $u_A > u_H$
after the black hole evaporates completely, we find that entanglement island
still exists and $\partial I$ is located on an equal-time Cauchy surface of the
observer $A$ when $r_{(A)}^2\geq64G_N\kappa c $.
