mathematical notation for defining a variable inside a conditional expression

I have the following conditional expression on $f$ and I want to use a variable which is only used inside the expression. I'm wondering what would be the best typset for defining it there.

Here is the expression and $\beta$ needs to be defined here.

$f=\begin{cases} 0,& \text{if } \alpha\geq 1\\ \beta+4, & \text{otherwise}, \text{(here is the question, where to put the definition) }, \beta:=\text{some expressions} \end{cases}$

can I say,

$f= \begin{cases} 0,& \text{if } \alpha\geq 1\\ \beta+4, & \text{otherwise}, \\ \beta:=\text{some expressions}, \end{cases}$

Or,

$f= \begin{cases} 0,& \text{if } \alpha\geq 1\\ \beta+4, & \text{otherwise}, \\ \text{where } \beta:=\text{some expressions}, \end{cases}$

Or maybe,

$f= \begin{cases} 0,& \text{if } \alpha\geq 1\\ \beta+4, & \text{otherwise},~ \beta:=\text{some expressions}, \end{cases}$