How did Hannah’s prayer lead to Samuel’s birth in the biblical account?

In the biblical account, Samuel was born to Hannah, who was one of the two wives of Elkanah and had previously been childless.123

Deeply distressed by her childlessness, Hannah traveled to the shrine at Shiloh, the center of the tribal confederacy, to pray for a son. During her prayer, she made a solemn vow to God: if she were granted a son, she would dedicate him to Yahweh for lifetime service.13

Her prayer was answered, and she gave birth to a son whom she named Samuel, a name interpreted as "Asked of God". True to her vow, once the boy was weaned, Hannah brought him to the shrine at Shiloh to be trained for service under the priest Eli.231