We report the observation and analysis of the 3 (3)ΠΩ double-minimum electronic excited state of (39)K(85)Rb. The spin-orbit components (0(+), 0(-), 1, and 2) of this state are investigated based on potentials developed from the available ab initio potential curves. We have assigned the vibrational levels v' = 2-11 of the 3 (3)Π1,2 potentials and v' = 2-12 of the 3(3)Π0(+/-) potential. We compare our experimental observations of the 3 (3)ΠΩ state with predictions based on theoretical potentials. The observations are based on resonance enhanced multiphoton ionization of ultracold KRb in vibrational levels v" = 14-25 of the a (3)Σ(+) state. These a-state ultracold molecules are formed by photoassociation of ultracold (39)K and (85)Rb atoms to the 5(1) state of KRb followed by spontaneous emission to the a state.