I have argued with friends that the verb: "to doubt" is not a synonym for the verb: "to suspect"; contrarily, it is actually opposite in meaning to the verb: "suspect".
Also, the noun: "doubt" does not mean "suspicion", but the opposite of it.
I agree- the only sort of instance where their meanings might seem to cross is an exchange like this:
A: 'I doubt it'll snow today.'
B: 'No, I suspect you're right.'
But the possibilities are about different things: the negation of snow, and A's positive prediction. So even though they seem similar, they're different.
b
I don't trust George. I doubt his honesty and suspect him of lying. I suspect he is dishonest and doubt he is telling the truth.
Even though I am conveying the same ideas, I am doing it in opposing ways. It is obvious that "I doubt that you are honest" and "I suspect that you are honest" are opposite in meaning.