The Houtborg triplets were not in fact triplets, but a set of fraternal twins, Fiona and Amavet and a third child, a girl named Adela. The three children were born at roughly the same time at the fort of Houtborg where Riannon, the mother of the twins was imprisoned and Falka, Adela's mother was quartering during a rebellion.
Riannon went quite mad even before the children were born and Falka abandoned her daughter to the mad prisoner's care to continue with the rebellion. Riannon, while able to care for the children, could not tell them apart and therefore never knew which two were in fact her own.
When she was finally freed by her husband, king Goidemar's troops and brought home, the king hired several mages to determine which of the children were his. The mages did succeed but decided not to reveal their findings as that would have meant the execution of a two year old child.