By multiplication rule of probability,
$P(A_1\cap A_2)=P(A_1)P(A_2/A_1)$
Now,
$P(A_1\cap A_2\cap A_3)=P(A_1\cap A_2)P(A_3/(A_1\cap A_2))$
Substituting the value of $P(A_1\cap A_2)$,
$P(A_1\cap A_2\cap A_3)=P(A_1)P(A_2/A_1)P(A_3/(A_1\cap A_2))$
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