A new detection system for the measurement of beta-delayed neutron emission probabilities has been characterized using fission products with well known β-delayed neutron emission properties. The setup consists of BELEN-20, a 4π neutron counter with twenty 3He proportional tubes arranged inside a large polyethylene neutron moderator, a thin Si detector for β counting and a selftriggering digital data acquisition system. The use of delayed-neutron precursors with different neutron emission windows allowed the study of the effect of energy dependency on neutron, β and β-neutron rates. The observed effect is well reproduced by Monte Carlo simulations. The impact of this dependency on the accuracy of neutron emission probabilities is discussed. A new accurate value of the neutron emission probability for the important delayed-neutron precursor 137I was obtained, Pn = 7.76(14)%.