Description of Markov Related Theorems
If $X$ is a nonnegative random variable and $a>0$, then the probability that $X$ is at least $a$ is at most the expectation of $X$ divided by $a$: $$ P(X\ge a) \le \frac{\mathbb{E}[X]}{a} $$
Expectation can be decomposed into two parts $\mathbb{E} = \Big( P(X<a) \cdot \mathbb{E}[X|X<a] \Big) + \Big( P(X\ge a) \cdot \mathbb{E}[X|X \ge a] \Big) $ As $\mathbb{E}[X|X \ge a]$ is larger than or equal to $a$, hence intuitively,
\(\begin{aligned} \mathbb{E}(X) &\ge \Big( P(X\ge a) \cdot \mathbb{E}[X|X \ge a] \Big) \\ &\ge P(X\ge a) \cdot a \end{aligned}\) and \(\Rightarrow P(X \ge a) \le \frac{\mathbb{E}(X)}{a}.\)