To simplify the expression, we need to first expand the denominator of the fraction, which is \((3x)^3\). This can be written as \(3^3 x^3\) or \(27x^3\).
Substituting this in the original fraction gives:
$$\frac{3x^3}{(3x)^3} = \frac{3x^3}{27x^3} = \frac{1}{9}$$
Therefore, the simplified form of the expression is \(\frac{1}{9}\).
Hence, the correct option is \(\frac{1}{9}\).