Both Uses of

conjecture
in
Henry IV, Part 2

Rumour is a pipe Blown by surmises, jealousies, conjectures, And of so easy and so plain a stop That the blunt monster with uncounted heads, The still-discordant wavering multitude, Can play upon it.†
Scene 1.1

conjectures = guesses (opinions based on inconclusive evidence)

Conjecture, expectation, and surmise
Of aids incertain should not be admitted.
Scene 1.3 *

conjecture = conclusion or opinion based on inconclusive evidence

Definition:

a conclusion or opinion based on inconclusive evidence; or the act of forming of such a conclusion or opinion

A conjecture can be widely believed, but the word is also frequently used to imply that evidence is insufficient to support a belief.