Let $m_1$ and $m_2$ be the slopes of line $O M$ and line $M B$.
Hence $m_1=\frac{4-\frac{5}{2}}{5-\frac{7}{2}}=1$
Since $O M \perp M B$
Hence $m_1 m_2=-1$
$$
\Rightarrow m_2=-1
$$

Hence equation of line $A B$ can be written as,
$$
\begin{aligned}
& \Rightarrow\left(y+\frac{5}{2}\right)=(-1)\left(x+\frac{7}{2}\right) \\
& \Rightarrow x+y+\frac{5}{2}+\frac{7}{2}=0 \\
& \Rightarrow x+y+6=0
\end{aligned}
$$
$\Rightarrow \frac{1}{6} x+\frac{1}{6} y+1=0$ ...(i)
But $a x+b y+1=0$ (given) is also the equation of chord $A B$ Hence $a=\frac{1}{6}, b=\frac{1}{6}$ $\Rightarrow 3 a+3 b=3\left(\frac{1}{6}\right)+3\left(\frac{1}{6}\right)=1$