Distilled water is not conductive...I believe you are confusing distilled water with de-ionized water
what is conductive in drinkable water is the ions in it that
act as electrons...
They are both purified, just different methods of doing it.
Distilled water is often defined as bottled water that has been produced by a process of distillation and has an electrical conductivity of not more than 10 µS/cm and total dissolved solids of less that 10 mg/L. Distillation involves boiling the water and then condensing the steam into a clean container, leaving most solid contaminants behind. Distillation produces very pure water but also leaves behind a leftover white or yellowish mineral scale on the distillation apparatus, which requires that the apparatus be frequently cleaned. Distillation does not guarantee the absence of bacteria in drinking water; unless the reservoir and/or bottle are sterilized before being filled, and once the bottle has been opened, there is a risk of presence of bacteria.
For many applications, cheaper alternatives such as deionized water are used in place of distilled water.
Double-distilled water (abbreviated "ddH2O", "Bidest. water" or "DDW") is prepared by double distillation of water. Historically, it was the de facto standard for highly purified laboratory water for biochemistry and trace analysis until combination methods of purification became widespread.
Deionized water which is also known as demineralized water (DI water or de-ionized water; can also be spelled deionised water, see spelling differences) is water that has had its mineral ions removed, such as cations from sodium, calcium, iron, copper and anions such as chloride and bromide. Deionization is a physical process which uses specially-manufactured ion exchange resins which bind to and filter out the mineral salts from water. Because the majority of water impurities are dissolved salts, deionization produces a high purity water that is generally similar to distilled water, and this process is quick and without scale buildup. However, deionization does not significantly remove uncharged organic molecules, viruses or bacteria, except by incidental trapping in the resin. Specially made strong base anion resins can remove Gram-negative bacteria. Deionization can be done continuously and inexpensively using electrodeionization.
It should be noted that deionization does not remove the hydroxide or hydronium ions from water; as water self-ionizes to equilibrium, this would lead to the removal of the water itself.