Urn $I$ contains $3$ white, $2$ black and $2$ green balls, Urn $II$ contains $2$ white, $3$ black and $4$ green balls, Urn $III$ contains $5$ white, $2$ black and $2$ green balls. An urn is chosen at random and two balls are drawn, they happen to be black and green. Probability that they come from Urn $II$ is:

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