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SYDNEY, Australia — The tabloids in Australia called Kathleen Folbigg a murderer of innocent babies — the nation’s “worst female serial killer.” In 2003, a court sentenced her to 40 years in prison for smothering her four children before each had turned 2.

But all along, Ms. Folbigg has insisted that she is innocent, and that her children were all victims of Sudden Infant Death Syndrome.

Now, 90 leading scientists say they’re convinced she is right. New genetic evidence, the scientists say, suggests that the children died from natural causes, and they are demanding that she be pardoned.

In a petition sent to the governor of New South Wales last week, the group of scientists, which includes two Nobel laureates, called for Ms. Folbigg’s immediate release and an end to the “miscarriage of justice.”

The very public challenge sets up a tense standoff between some of the world’s top medical minds and a criminal court system that rarely overturns convictions. It’s a story of judges putting more weight on the ambiguous musings of a mother’s diary than on rare genetic...