The question, as I understand it, is why is electricity dangerous around water. The answer to the dangerous part has to do with how electricity kills. Aside from large currents which turn you into a crispy critter, the danger comes from the current that flows through your heart (all that blood and fluids in your body are pretty good conductors). So, these are general rules only. Don't try this to see if it's OK.
If a current greater than 5 mA flows through your heart, it will (usually) put your heart into irregular beats (fibrillation) or (less often) stop it all together. Both kill you, fibrillation a little more slowly.
Dry skin resistance can be as high as 100,000 Ohms (and that depends on the actual voltage and changes with the current, etc but isn't important here). Wet skin resistance can be as low as 1000 Ohms (or much less depending on your skin). And that doesn't much depend on whether you have spring water, recently deionized water, boiled water, etc.
So, if you're in the bathtub, your skin resistance is about 1000 Ohms, and you're using the 120VAC electric shaver and drop it in the water, the current will be about 120 mA and it has the opportunity to flow through your heart (maybe in the left arm and out the left leg which are both wet - who knows?). This will likely kill you. If you're interested, Google the death of the monk/author Thomas Merton.
Ground Fault Current Interrupter circuits are required in the US wherever you have wet conditions - bathroom, kitchen, basement, outside, etc - and they work by quickly opening whenever the "extra" current (that is, the difference between the currents in the hot and neutral wires) reaches 5 mA.