Ultrafast reflection and secondary ablation have been theoretically investigated with a Fresnel-Drude model in laser processing of transparent dielectrics with picosecond pulsed laser. The time-dependent refractive index has a crucial effect on the cascade ionization rate and, thereby, on the plasma generation. The relative roles of the plasma gas and the incident angle in the reflection are discussed in the case of the oblique incidence. The angular dependence of the reflectivity on the laser-excited surface for s- and p-polarization is significantly different from the usual Fresnel reflectivity curve in the low-fluence limit. A road map to the secondary ablation induced by the reflected pulse is obtained on the angles of the first and second incidence. It indicates that the laser-induced plasma plays a major role in the secondary ablation, which could overcome the saturation of the ablation crater depth or generate microcracks underneath the crater wall.