The Collaborative International Dictionary of English v.0.48:

Likely \Like"ly\, a. [Compar. Likelier (l[imac]k"l[i^]*[~e]r);
   superl. Likeliest.] [That is, like-like. See Like, a.]
   1. Worthy of belief; probable; credible; as, a likely story.
      [1913 Webster]

            It seems likely that he was in hope of being busy
            and conspicuous.                      --Johnson.
      [1913 Webster]

   2. Having probability; having or giving reason to expect; --
      followed by the infinitive; as, it is likely to rain.
      [1913 Webster]

   3. Similar; like; alike. [Obs.] --Spenser.
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   4. Such as suits; good-looking; pleasing; agreeable;
      handsome. --Shak. --Milton.
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   5. Having such qualities as make success probable; well
      adapted to the place; promising; as, a likely young man; a
      likely servant.
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   6. Improbable; unlikely; -- used ironically; as, a likely
      story. [informal]
      [PJC]