Conjecture, surmise, guess are comparable as verbs, meaning to draw an inference from slight evidence, and as nouns, denoting an inference based upon such evidence.
Conjecture implies formation of an opinion or judgment upon what is recognized as insufficient evidence.
Surmise implies still slighter evidence, and exercise of the imagination or indulgence in suspicion.
Guess implies a hitting upon or an attempting to hit upon either at random or from insufficient, uncertain, or ambiguous evidence.