"Suspect" means "think". But more specifically, it means "think that someone did something wrong" or "think that something bad has happened". You can use this word when you think someone did something bad, but you're not sure. For example:
I'm starting to suspect that she's been cheating on me.
In this example, you don't know for sure that she's cheated, but there is some evidence that makes you think it might be true.
However, there's another use of the word "suspect" when you're just making guesses about the future. This use isn't as common. It's used like this:
I suspect it might rain later this afternoon.
It's most common to use "suspect" for guessing about negative things like bad weather.
When your level of suspicion is high, you say that you "strongly suspect that ___"