The Collaborative International Dictionary of English v.0.48:

Possibility \Pos`si*bil"i*ty\, n.; pl. Possibilities. [F.
   possibilit['e], L. possibilitas.]
   1. The quality or state of being possible; the power of
      happening, being, or existing. "All possibility of error."
      --Hooker. "Latent possibilities of excellence." --Johnson.
      [1913 Webster]

   2. That which is possible; a contingency; a thing or event
      that may not happen; a contingent interest, as in real or
      personal estate. --South. Burrill.
      [1913 Webster]

WordNet (r) 3.0 (2006):

possibility
    n 1: a future prospect or potential; "this room has great
         possibilities"
    2: capability of existing or happening or being true; "there is
       a possibility that his sense of smell has been impaired"
       [syn: possibility, possibleness] [ant: impossibility,
       impossibleness]
    3: a tentative insight into the natural world; a concept that is
       not yet verified but that if true would explain certain facts
       or phenomena; "a scientific hypothesis that survives
       experimental testing becomes a scientific theory"; "he
       proposed a fresh theory of alkalis that later was accepted in
       chemical practices" [syn: hypothesis, possibility,
       theory]
    4: a possible alternative; "bankruptcy is always a possibility"
       [syn: possibility, possible action, opening]

Moby Thesaurus II by Grady Ward, 1.0:

44 Moby Thesaurus words for "possibility":
   admissibility, aptitude, aptness, best bet, capacity, chance,
   conceivability, contingency, delitescence, dormancy, eventuality,
   favorable prospect, feasibility, good chance, good opportunity,
   good possibility, latency, latent content, latent meaningfulness,
   latentness, liability, liableness, likelihood, likeliness,
   main chance, obligation, odds, odds-on, odds-on chance,
   opportunity, plausibility, possibilities, potential, potentiality,
   probability, promise, proneness, prospect, sporting chance,
   sure bet, sure thing, virtuality, weakness, well-grounded hope



Bouvier's Law Dictionary, Revised 6th Ed (1856):

POSSIBILITY. An uncertain thing which may happen; Lilly's Reg. h.t.; or it
is a contingent interest in real or personal estate. 1 Mad. Ch. 549.
     2. Possibilities are near as when an estate is limited to one after the
death of another; or remote, as that one man shall be married to a woman,
and then that she shall die, and he be married to another. 1 Fonb. Eq. 212,
n. e; l6 Vin. Ab. h.t., p. 460; 2 Co. 51 a.
     3. Possibilities are also divided into, 1. A possibility coupled with
an interest. This may, of course, be sold, assigned, transmitted or devised;
such a possibility occurs in executory devises, and in contingent, springing
or executory uses.
     4.-2. A bare possibility, or hope of succession; this is the case of
an heir apparent, during the life of his ancestor. It is evident that he has
no right which he can assign, devise, or even, release.
     5.-3. A possibility' or mere contingent interest, as a devise to Paul
if he survive Peter. Dane's Ab. c. 1, a 5, Sec. 2, and the cases there
cited.