Probability of retirement event This is elementary, but not clear to me.

Suppose I know that the mean age of retirement is $\mu$ and the standard deviation $\sigma$.
What is the probability that someone of age $x$, who has not yet retired, 
will retire sometime in the next year,
i.e., between $x$ and $x+1$?

Clearly for small $x$, far below the mean, the probability is near zero, and for large $x$, it approaches $1$.  So it is a type of cumulative distribution...

Thanks for your help!
\begin{align}
\mathbb{P}(X \in [x,x+1) \vert X \geq x) &amp; = \dfrac{\mathbb{P}(X \in [x,x+1))}{\mathbb{P}(X \geq x)} = \dfrac{F_X(x+1) - F_X(x)}{1-F_X(x)}\\
&amp; = 1 - \dfrac{1-F_X(x+1)}{1-F_X(x)}
\end{align}
Since you have not clarified if you are looking for a bound on the probability, this is what we get.
Integrate the Gaussian probability density function from x to x+1