The fusion probability in hot fusion reactions leading to the synthesis of super-heavy nuclei are investigated systematically. Based on the quasi-fission barrier height obtained with the Skyrme energy-density functional, we propose an analytical expression for description of the fusion probability, with which the measured evaporation-residual cross sections can be reproduced acceptably well. Simultaneously, some special fusion reactions for synthesizing new elements 119 and 120 are studied. The predicted evaporation-residual cross sections for 50Ti+249Bk are about 10~150 femtobarn at energies around the entrance-channel Coulomb barrier. For the fusion reactions synthesizing element 120 with projectiles 54Cr and 58Fe, the cross sections fall to a few femtobarn which seems beyond the limit of the available facilities.