# How do I draw a DFA diagram when I only care about how the string ends?

Hi so this is my first week learning about automata and I have an exercise I'm going through. I'm supposed to draw a diagram for the DFA that accepts all strings of a and b where the third last symbol is a b. So it's like : $\{a,b\}^*b\{a,b\}^2$ right?

And if I would draw it I would do this to check the end:

I believe this to be correct but I'm not sure how to draw the possibilites of a's and b's beforehand