linear constraint on binary variable

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I have to make a linear constraint for a binary variable in the following way.

We have a set $S=\{0,1,\dots,k\}$ and the binary variable $b$ is defined as:

$$b=\begin{cases} 1 & if\;S=1,\\ 0 & otherwise \end{cases} .$$

I couldn't manage to create the constraints for this relation to hold.