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Small question on exponential distribution

Let $X$ be a random variable and the duration of a phone call. We know that already $1$ minute has passed. How big is the probability that the phone call goes on for $3$ additional minutes? The CDF is $$F(x)=1-e^{(-1/4\cdot x)}$$

So my thought is to use the formula for the conditional probability:

$$P(X \ge 4 | X > 1) = \frac{P(X \ge 4 \cap X > 1)}{P(X > 1)}$$

I know that $P(X > 1)= e^{(-1/4)}$ but I'm not sure how to compute $P(X \ge 4 \cap X > 1)$. Is this the same probability as $P(X\ge4)$? I mean if $4$ minutes pass, this also implies that $1$ minute has passed.

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    Yes, you're right about $X\ge4 \implies X>1$ – 2017-02-18
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    @GNU Supporter Thank you – 2017-02-18

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$P(X \geq 4 \cap X>1) = P(X \geq 4)$ since $\{X \geq 4\} \subset \{X >1\}$.