Amanita, let's carefully solve the problem step by step.

Step 1: Understanding the Problem We are given the inequality:

$\left(\frac{1}{3}\right)^x \geq \left(\frac{1}{3}\right)^{0.2}$

We need to find all values of $x$ that satisfy this inequality and choose the correct interval from the options.

Step 2: Analyzing the Bases Both sides have the same base, $\frac{1}{3}$, which is a positive number less than 1. For exponential inequalities with a base between 0 and 1, the direction of the inequality sign reverses when comparing exponents.

Step 3: Setting Up the Exponent Inequality Since the base is less than 1, the inequality reverses:

$$x \leq 0.2$$

Step 4: Writing the Solution as an Interval The solution to $x \leq 0.2$ in interval notation is $(-\infty, 0.2]$.

Step 5: Matching with the Provided Options Let's check which option matches $(-\infty, 0.2]$.

Now, let's solve the inequality using a tool to confirm our reasoning. Amanita, after solving the inequality, we find that the solution is $x \leq 0.2$ (since $0.2 = \frac{1}{5}$). In interval notation, this is written as $(-\infty, 0.2]$.

From the options given, the correct answer is:

$$x \in (-\infty; 0.2]$$