When flipping a fair coin twice, each flip has two possible outcomes: heads (H) or tails (T).

The sample space is given by

$$S=\{HH,HT,TH,TT\}$$

Let $E$ be the even of getting two heads, then

$$E=\{HH\}$$

Thus, the probability of getting two heads in a row is given by

\begin{align*}
P(E) &= \frac{n(S)}{n(E)}\\
&= \frac{1}{4}.
\end{align*}

Therefore, the probability of getting two heads in a row when flipping a fair coin twice is $\frac{1}{4}$.