It is fairly easy to build a high voltage probe for a multimeter, at least for measuring DC and low-frequency AC. You just solder together a series string of high-value resistors and place them inside a small PVC tube of appropriate length. I happen to have a bunch of surplus 100+ megohm resistors that I often jury-rig as a temporary high-voltage divider. You can also purchase high voltage probes for multimeters at fairly reasonable prices. Tektronix has a high-voltage probe for oscilloscopes, but it is a bit pricy.
So, I can see why you would want to "steal" a little power from your electric fence to run a Rat Zapper. That does sound like it would be doable, but I don't know what kind of voltage the electric fence provides... is it in the form of high-frequency AC pulses? I do know the fence voltage must be current-limited by design, but some research is necessary to determine how that is done and how it would affect your ability to "charge up" a Rat Zapper.
IMO it would take a significant amount of energy to effectively electrocute a rat. One pulse per second from the electric fence is not going to do the job. You would have to store that energy in a capacitor and then wait to discharge it through the rat. It may take several minutes to accumulate enough charge from the fence to do the job, so it would have to be a "one-shot" discharge of sufficient amplitude and duration, perhaps as long as two minutes, before it could "fire" again. Of course if it kills the rat in two minutes there is no need to recharge that particular trap until you dispose of the rat. There is also the minor problem of automagically disconnecting it from the fence after it kills a rat and before you empty the trap. That might be necessary to allow multiple devices to operate at the same time from the fence wire. I would also add a little LED to indicate the device was on and had NOT been triggered. LED off: dead rat inside.
Do you have any information on the electric fence you are using, such as model number, length of wire it is designed to energize, etc? It is likely that you will need some high-voltage rectifiers as well as largeish capacitors to obtain and store power from the fence. This stored power would possibly have to be increased in voltage with a DC-to-DC converter to provide sufficient voltage and current to electrocute a rat, so we are getting into a more expensive design area. It might make more economic sense to buy a commercial Rat Zapper and then figure out a way to power it from your electric fence rather than the batteries it was designed to use. I am sure there would be a commercial market for such a "power converter" device, so that is the first thing I would consider building. Just set your RZ on the ground and clip the "power converter" wire to your electric fence. A few minutes of "charging" and it is good to go.
If I haven't made it clear yet, the electric fence doesn't provide enough power to electrocute a rat. This is by design. You need to take power from the fence at whatever rate it will provide and save it up in a capacitor (or a re-chargeable battery, but I would avoid that) until the stored energy is delivered to the rat in sufficient quantity and duration to ensure the rat is killed. We can probably help you with that here.