It is a general belief in apertureless near-field microscopy that the so-calledp-polarization configuration, where the incident light is polarized parallel to the axis of the probe, is advantageous to its counterpart, thes-polarization configuration, where the incident light is polarized perpendicular to the probe axis. While this is true for most samples under common near-field experimental conditions, there are samples which respond better to thes-polarization configuration due to their orientations. Indeed, there have been several reports that have discussed such samples. This leads us to an important requirement that the near-field experimental setup should be equipped with proper sensitivity for measurements withs-polarization configuration. This requires not only creation of effective s-polarized illumination at the near-field probe, but also proper enhancement of s-polarized light by the probe. In this paper, we have examined thes-polarization enhancement sensitivity of near-field probes by measuring and evaluating the near-field Rayleigh scattering images constructed by a variety of probes. We found that thes-polarization enhancement sensitivity strongly depends on the sharpness of the apex of near-field probes. We have discussed the efficient value of probe sharpness by considering a balance between the enhancement and the spatial resolution, both of which are essential requirements of apertureless near-field microscopy.