1. From q0:
δ(q0, a, Z0) = (q1, Z0, 1Z0)
2. From q1:
δ(q1, a, Z0) = (q2, Z0, 1Z0)
δ(q1, a, 1) = (q2, 1, 11)
3. From q2:
δ(q2, a, 1) = (q1, 1, 1)
δ(q2, b, 1) = (q3, 1, λ)
4. From q3:
δ(q3, b, 1) = (q3, 1, λ)
δ(q3, λ, Z0) = (q4, Z0, Z0)
q0 is initial state and also q4 is final state.
At first we should be sure that we have at least 2 a's then one b. Then we can use a loop for more a's.