I have an insert in my silverware drawer with 5 rectangular sub-trays, front to back for utensils, and one smaller one, integral to the assembly that sits in back, left-to-right. I keep my probes in there. I've never felt the need to protect them/myself, but mine aren't overly sharp either.
A cork could be quartered lengthwise and one used for 4 probes if you were so inclined.