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The intermediate valence compound YbAl$_3$ is known to undergo a hybridization process between itinerant and localized electrons. The resulting heavy Fermi liquid remains non-magnetic and non-superconducting. A microscopic understanding of the hybridization process in YbAl$_3$ is still lacking although some characteristic temperature and energy scales have been identified. Here we report results from novel spectroscopic measurements based on quasiparticle scattering. From the conductance spectra taken over a wide temperature range, we deduce that the band renormalization and hybridization process begins around 110 K, causing the conductance enhancement with a Fano background. This temperature, a new scale found in this work, is much higher than the coherence temperature (34 K). Our observation is in agreement with the slow crossover scenario discussed recently in the literature. The indirect hybridization gap appears to open concomitantly with the emergence of a coherent Fermi liquid. Thus, we suggest its measurement as a more rigorous way to define the coherence temperature than just taking the temperature for a resistivity peak.