We analyze the alpha-decay fine structure to excited 0(2)(+) states in Hg and Rn isotopes. These states are described as minima in the potential energy surface (PES) provided by the standard deformed Woods-Saxon plus pairing approach. We also investigate alpha decay from the excited state P(0(2)(+)) in the parent nucleus by evaluating the corresponding hindrance factor (HF). By analyzing the experimental HF's we find the remarkable property that the ground and excited states D(0(1)(+)) and D(0(2)(+)) in the daughter nuclei are occupied with almost equal probabilities if there is no excited P(0(+)) states in the parent nucleus. Moreover, if there exists an excited state P(0(2)(+)) then the occupation probability of this state is 25%.