Ideally it's best to check the progress of your fermentation with a hydrometer. This allows you to determine when fermentation is complete, and by knowing the starting and ending measurements, it's possible to make a reasonably accurate estimation of alcohol content. You can use the formula:
Alcohol by Volume = (1.05/0.79) x ((OG – TG) / TG) x 100
Where OG is the Original Gravity measurement - taken before fermentation begins, and FG Final Gravity, is the current reading. If your mix is alcohol & water, you can also use an Alcoholmeter, which is a type of hydrometer.
You may be able to taste your wash, and roughly judge how much sugar is left. If it's still sweet at all, the ferment is not finished. That's not to say the yeast has not given up though!
Ok, so you're 3 days in. It's impossible to say accurately, but primary fermentation generally lasts 3-7 days (in beer brewing). But you're fermenting plain sugar which does not have any nutrients for the yeast, so we can expect a sub-optimal fermentation.
There's obviously nothing to stop you distilling this right now, it's probably got some alcohol in it. But if you wish to somewhat optimise the yield, it may be better to wait 7 days, or even two weeks.
The cloud in the wash will clear as the yeast settles out. But from what I can research, it seems a common practice to distill a wash made from pure sugar while it's cloudy.