GY, The probe tip is obviously the most 'cooled' part of the assembly and therefore the most susceptible to icing.
Not necessarily so for ice crystals. Some regulatory thoughts on
probe icing. The small ice crystals might either block the tube because of the density of an accumulation jam up, or some crystals melt and act as the glue for others to adhere to an ice or ice / water block.
Thus the coolest point of a probe may not be the most likely place for ice crystal icing; the crystals tend to bounce off a cool dry surface.
The mechanics of the icing also depend on the crystal size or mass, the airflow path before and in the probe, and the anti-ice heating capability - heat flow.