Special formulas for an efficient computation of first-flight escape and transmission probabilities in X-Y-Z geometry are presented. The approach used to derive these formulas is based on rearranging and grouping similar terms in the general three-dimensional formulas reported in a previous work by the author. When applied to fine grids, the new formulas are found to be orders of magnitude more efficient than the original ones. Numerical results are reported for test cases defined by regular hexahedra of various optical dimensions, including one where partitions are used to define the source and sink zones in the calculations of the escape and transmission probabilities.