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How to assume the sum of some variables is equal to a constant?

Suppose I have this expression:

$$\frac{a {\left(t_{1} + t_{2} + t_{3} - 1\right)}}{b} $$

This can be simplified to 0 if we assume $t_1 + t_2 + t_3 = 1$.

How can I accomplish this in Sage? I've tried:

var('t1', 't2', 't3', 'a', 'b')
expr1 = ((t1 + t2 + t3 - 1)*a)/b

assume(t1 + t2 + t3 == 1)

I expected the second call tofull_simplify() to return 0 but it returned the same result as the first call, which is $$\frac{a t_{1} + a t_{2} + a t_{3} - a}{b}$$