How does priestly make such a striking ending to the play?

The family is so relieved that the Inspector's visit is what they believed to be a hoax that they never expect what comes next. When the phone rings, everyone is happy and enjoying their morning. Birling answers it, listens, and puts the phone down. Looking at the others, panic-stricken, he utters the play’s final lines:

“That was the police. A girl has just died—on her way to the Infirmary—after swallowing some disinfectant. And a police inspector is on his way here—to ask some—questions—”