With the emitter/gap-potential/tip structure, we have studied the hot electron (HE) transmission properties used in scanning hot electron microscopy (SHEM). The rational and practical gap potential profile between two electrodes has been constructed based on the electrostatic image force and the jellium model. The transmission probability calculated using the constructed potential profile in this paper differs from that using conventional profiles appreciably. Dependencies of the transmission probability on the gap separation, HE energy, and the tunnel voltage have been made clear.