Before I answer your question, welcome to World Building. This community is related to Science Fiction in many ways, but here we answer and discuss questions related to building an environment according to your requirements.
Your world focuses on an alternate Earth, where Earth has gone through some major changes from what it is now in real world. In particular, you ask:
1- ... with something as close as to 20-40% of all its surface water. Would be that believable?
If that is believable or not, depends on the type and severity of the disaster which fell upon Earth. If the type of disaster is correct, then it will definitely be believable.
For example, if Earth was hit by a series of extremely large (~15 km diameter) asteroids, that would release immense amount of heat, equal to millions of atomic bomb explosions. The temperature required to break up water into hydrogen and oxygen is about 2000 °C. In case of a mega disaster, a large amount of Earth's water will decompose into hydrogen and oxygen. Hydrogen will rise up in the atmosphere and will slowly be lost into space (hydrogen often escapes into space due to solar wind, from the atmosphere of low gravity planets like Earth). This will leave behind an Earth which is completely different from the Earth we know. A lot of water would be lost, but the atmosphere would be extremely rich in oxygen. I have not done any calculations about it, but my crude guess is that 90% of the atmosphere (by mass) would be oxygen. Also remember, that a disaster of this scale will wipe out everything other than extremophile bacteria. There will be nothing larger than amoeba left alive in the oceans or on the land. The climate would undergo extreme changes and the whole planet will probably undergo an ice age for tens of millions of years. Only the people up in the satellites would survive such a disaster. All the others (even the last man on Earth) would die within one year after the first 15 km asteroid falls.
Another, less damaging method of removing surface water could be by some sort of new bacteria. The bacteria breaks down water into oxygen and hydrogen, and then uses hydrogen in respiration. This bacteria thrives in the oceans and rivers/lakes and begins to decompose water into hydrogen and oxygen in large quantities. Scientists program a virus to kill that bacteria only. After many decades, all the bacteria of that kind are killed, but they have already decomposed 60% of Earth's water. This will again leave a planet very very different than what it is today. Almost all of the humans and other creatures will die. The only humans surviving the global change will be living deep in shelters with artificial environment.
So yes. If you plan your disaster nicely, it will be believable. Heck! If movies like Looper and Matrix can be believable, your idea will be believed too.
2- Or for most people it would seem like a impossible condition for sustaining life, even on a ridiculous small amount?
Yes, most of the humans with our current body structure will die. Very few can survive, but they will be living under hellish conditions. Seasons will be extremely severe and wind storms will be far more powerful than anything we know today. Usually the wind and dust storms will blow over areas as large as whole continents.
3- Also, if possible what would be the smaller percentage that I could use and still keep it believable?
You could go on and remove all the water from your world if you want. Most of the things in science fiction are not possible under current scientific knowledge, that is why it is fiction.
Just keep in mind that all life forms on our planet require water for survival. If people and animals don't get drinkable water, they die. If plants don't get enough water in the soil, they die. If plants die, animals die because there are no plants to eat. If there is no rain (due to too less surface water), many bad things will happen to the large scale climate and a lot of plants and animals will go extinct. If you only want to keep a few people in far off places to survive in artificial conditions, you could go on and remove 85% of all water on the planet. Earth will become hellish and most animals will die. Most of the plants will die too. The surviving people will need to have their facilities located near the small seas and convert seawater into freshwater to survive. They will have to keep fish and cattle in small areas and grow crops too. It will be possible with advanced technology, but it will only support small groups of people, located far away from one another, near seas and rivers.