Suppose if we pick odd $a,b$ randomly in $(t_1,t_2)$ where $0<t_1<b<a<t_2<\infty$ holds the probability that $(a,b)=1$ holds is $\frac1{\zeta(2)}$.
What is the probability that if we pick odd $a,b$ randomly in $(t_1,t_2)$ where $0<t_1<b<a<t_2<\infty$ holds then $(a,b)=(\frac{a+b}2,\frac{a-b}2)=1$ holds? Is it $\frac1{\zeta(2)^2}$?