Theoretical physicists may debate whether the universe is random or not, but for practical purposes it is, because any sufficiently complicated deterministic system looks random to someone who does not fully understand it. This is the example from Lipman (1991) “How to decide how to decide…”: the output of a complicated deterministic function that is written down still looks random to a person who cannot calculate its output.
If the world is random, we should not put probability one on any event. Nothing is certain, so any fanatical belief that some claim is certainly true is almost certainly wrong. This applies to religion, ideology, personal memories and also things right before your eyes. The eyes can deceive, as evidenced by the numerous visual illusions invented and published in the past. If you see your friend, is that really the same person? How detailed a memory of your friend’s face do you have? Makeup can alter appearance quite radically (http://www.mtv.com/news/1963507/woman-celebrity-makeup-transformation/).
This way lies paranoia, but actually in a random world, a tiny amount of paranoia about everything is appropriate. A large amount of paranoia, say putting probability more than 1% on conspiracy theories, is probably a wrong belief.
How to know whether something is true then? A famous quote: “Everything is possible, but not everything is likely” points the way. Use logic and statistics, apply Bayes’ rule. Statistics may be wrong, but they are much less likely to be wrong than rumours. A source that was right in the past is more likely to be right at present than a previously inaccurate source. Science does not know everything, but this is not a reason to believe charlatans.