ない　(or 無い）　generally means there isn't or something does not exist (first meaning). e.g. お金がない。　(there isn't any money). Also, it negates a verb or an adjective （second meaning) (いく="to go" but いかない="to not to go". (you cannot say いくない。It has to be conjugated). あかい　＝　red.　あかくない　＝　not red. そう generally means "it seems." E.g. おいしい＝delicious. おいしそう＝it seems delicious. So considering above, I'll give some examples: お金がなさそう　＝　There doesn't seem to be any money. (The first meaning of　無い) おいしくなさそう　＝　it does not seem delicious.　(the second meaning) 天気よくなさそう　＝　the weather does not seem good (the second meaning) それは正しくなさそう　＝　That does not seem correct (the second meaning). Note that "it seems", in this context, is the process of guessing. I hope it helps.

The closest English term to なさそう is "unlikely".

it seems to be nothing. それはなさそうだ。(それは無さそうだ)