We report new results on the spectroscopy of the 3 (3)Σ(+) electronic state of (39)K(85)Rb. The observations are based on resonance-enhanced multiphoton ionization of ultracold KRb molecules starting in vibrational levels v'' = 18-23 of the a (3)Σ(+) state and ionized via the intermediate 3 (3)Σ(+) state. The a-state ultracold molecules are formed by photoassociation of ultracold (39)K and (85)Rb atoms to the 3(0(+)) state of KRb followed by spontaneous emission. We discuss the potential applications of this state to future experiments, as a pathway for populating the lowest vibrational levels of the a state as well as the X state.