Answer
$\frac{1}{232}$
Work Step by Step
We know that $probability=\frac{\text{number of favorable outcomes}}{\text{number of all outcomes}}$
The number of all outcomes is $(9+11+1+124)(9+11+1+124-1)=145\cdot144=20880$, because the first person can be anyone, the second can be anyone apart from the first one.
The number of good outcomes is $(9+1)(9+1-1)=10\cdot9=90$ because the first person has TB, the second also has TB but cannot be the first person.
Thus probability$=\frac{90}{20880}=\frac{1}{232}$