# example that conditional independence does not imply independence

can anyone help with an example for a PMF or some density that:

$$P(A,B|C)=P(A|C)P(B|C )$$ but $$P(A,B)\not=P(A)P(B)$$

Take any two events $$A$$ and $$B$$ which are not independent and take $$C=A$$.
Note that $$P(A,B|C)=\frac {P(A\cap B)} {P(A)}$$ and $$P(A|C)P(B|C)=(1)(\frac {P(A\cap B)} {P(A)}=\frac {P(A\cap B)} {P(A)}$$.