Transitions occur only when the energy gap matches with the incident light (quantum mechanics). Subjecting the molecule with higher energy will not increase the transition probability. Though in many cases we see absorption at higher energy because there exists higher energy level(s) with varying degree of overlap.
Agree with Peter's view especially "So what does it mean "no absorbance at higher energies compared to [some] energy?" I may suggest please read so many articles on Rh 6G, BGE and absorbance. Good Luck...