$3=\int_{b}^{4}\left(\frac{1}{x^{2}}\right) \cdot d x$

Step 1 ：Given the integral equation \(3=\int_{b}^{4}\left(\frac{1}{x^{2}}\right) \cdot d x\), we need to find the value of \(b\).

Step 2 ：First, we find the antiderivative of \(\frac{1}{x^{2}}\), which is \(-\frac{1}{x}\).

Step 3 ：Next, we evaluate this antiderivative at \(4\) and \(b\), giving us \(-\frac{1}{4}\) and \(-\frac{1}{b}\) respectively.

Step 4 ：We then set the difference of these two values equal to \(3\), resulting in the equation \(-\frac{1}{4} + \frac{1}{b} = 3\).

Step 5 ：Solving this equation for \(b\), we find that \(b = \frac{4}{13}\).

Step 6 ：So, the final answer is \(\boxed{\frac{4}{13}}\).