How did Solomon know that the woman was real mother of the child?

When the two women were fighting over the child, Solomon suggested that the child be cut in half, and each woman would be given half. The actual mother was horrified and fought against this decision, saying that the other woman could keep the child, to avoid its death. While the fake mother was encouraging Solomons decision, and saying that they could keep half a baby each. Solomon gave the child to the real mother, the woman that would rather give him up than see him dead.