One note about conductivity probe cleaning. Scientific/industrial conductivity probes are typically made with platinum-plated electrodes. The platinum coating is used because it is highly resistant to corrosion, but far easier to work with during manufacturing than gold (the most resistant-to-corrosion metal). I don't know for certain that hobbyist probes would have platinum electrodes, but since the cost of setting up a different manufacturing process just to save material costs for hobbyist-type equipment would be prohibitive, it's likely that all of ours are platinum electrodes.
The typical solution for cleaning platinum conductivity electrodes is so-called piranha solution - 3:1 concentrated sulfuric acid to 30% hydrogen peroxide. Both of the constituents of piranha solution would be quite dangerous for a hobbyist without scientific laboratory experience to use. So don't - 30% H2O2 is really nasty stuff (as is concentrated sulfuric acid).
For a conductivity probe that's installed in a kalk reactor, the fouling components as Randy noted would be calcium carbonate. So the sort of materials that hobbyists typically use to clean calcium carbonate deposits off of other equipment are suitable - e.g., citric acid or vinegar. For a conductivity probe used in the actual tank/sump, organic materials will be present in addition to (probably) calcium carbonate. Probes used in this location can also be cleaned with citric acid and a gentle abrasion with a soft brush and a neutral detergent solution such as Dawn/Joy dishwashing soap. Tougher organic deposits can be cleaned with an overnight soak in a basic solution, such as 0.1N sodium hydroxide.
There are a couple of common materials that reefers tend to have around that I would not recommend be used to clean platinum electrodes - bleach and hydrochloric (muriatic) acid. The reason to avoid using either is the presence of chlorides in the solutions. At least in theory, a long soak in either may etch the platinum electrodes - a little etching can be used to clean surfaces, but the exposure time, temperature and concentration is important and generally beyond the knowledge base of typical hobbyists.