I have this time-dependent wave function from solving a 3-component Schrodinger's equation, $$\psi(t)=-\frac{2}{9}(-2, 1, 2)^T+\frac{2}{9}e^{3i\omega t}(2,2,1)^T+\frac{1}{9}e^{-3i\omega t}(1, -2, 2)^T$$

Clearly, $\psi(0)=(1,0,0)^T$ but the question that I had was what was the probability that the system is again in this state at time $t$? I am assuming what they meant by "this state" was that $\psi=(1,0,0)^T$. How should I approach this, what do I need to integrate over?

I found out that $|\psi|^2=1$ i.e., the wave function is normalised but does that do much?