Divisible by 3

Number Theory Level 1

${\huge \color{#3D99F6}N = \color{#20A900} {123,4}\color{#D61F06}{F}\color{#20A900}{6,789}}$

If $\color{#D61F06} {F}$ is replaced with a digit from the set (0, 1, 2, 3, 4, 5, 6, 7, 8, or 9) at random, what is the probability that $\color{#3D99F6} {N}$ will be divisible by 3?