What is the probability that a 4-dimensional integer lattice point is the first?

${\color{#D61F06}\text{This problem's question:}}$ What is the probability that a 4-dimensional integer lattice point is the first such lattice point in that specific direction from the origin?

Any random 4-dimensional integer lattice point may be chosen where each integer coordinate may be any integer from $-\infty$ to $\infty$ .