Presumably she greatly wanted to conceive, and the conception was solely through divine grace, because either she or her husband were incapable of conception.
Those aren’t exactly prurient points, they indicate the holiness of John, who was the result of the grace, which was the answer to their prayers, which were presumably jointly made in sincerity.
No doubt she did, both out of personal desire for a child and "to take away my reproach among men."
"the conception was solely through divine grace
Unless I've totally misunderstood everything, the conception of John was through natural sex. The conception of Jesus by Mary was "solely through divine grace," no human father nor natural reproductive act involved.