You just need to know the probability of the complementary event:

\( \Pr\{|X| \geq a\} \leq \frac {E[|X|]} {a} \)

\( \iff \Pr\{|X| < a\} = 1 - \Pr\{|X| \geq a\} \geq 1 - \frac {E[|X|]} {a} \)

Not sure if this is useful or answering your question.

You may google several different types of "extensions" of this inequality if you are seeking them. A famous one of course is the Chebyshev's inequality.