The modern sense has been with this word since it arrived in English at the end of the 14th century, but from the outset it displayed a range of meanings. Its sense of "disquieting" died out in the 18th century, but it can be seen when Henry says "Let me be umpire in this doubtful strife" (Henry VI Part 1, IV.i.151). Already dying out in Shakespeare's time was its sense of "awful", as when Egeon talks about "A doubtful warrant of immediate death" (The Comedy of Errors, I.i.69). Its other old sense, of "fearful", developed in the mid-16th century and stayed till around 1800.
It turns up half a dozen times in the plays. This is the sense required when Olivia refers to her "doubtful soul" (Twelfth Night, IV.iii.27), or Lady Macbeth tells her husband, "Tis safer to be that which we destroy Than by destruction dwell in doubtful joy" (Macbeth, III.ii.7).
David Crystal is author, with Ben Crystal, of Shakespeare's Words, published by Penguin