A male rat is either doubly dominant (AA) or heterozygous (Aa), owing to Mendelian properties, the probabilities of either being true is ½. The male rat is bred to a doubly recessive (aa) female. If the male rat is doubly dominant, the offspring will exhibit the dominant characteristic; if heterozygous, the offspring will exhibit the dominant characteristic ½ of the time and the recessive characteristic ½ of the time. Suppose all of 3 offspring exhibit the dominant characteristic. What is the probability that the male is doubly dominant?