Intuition sigmoid function

Sigmoid function
I have real value
but I want to change it into probability
Probability should be from O to 1
Look like below

If we have function like above, we can change any real value to probability

$\frac{1}{1+e^x}$

Now we got convert function
Let's call it sigmoid function

$sigmoid\left(x\right)=\frac{1}{1+e^{-\left(x\right)}}=\frac{e^x}{e^x+1}$