Equilibrium state proof with lagrange

[Guffie]

Hello,

I have been trying to follow the start of these lecture notes I found online and I have having trouble understanding what is happening between two steps.

The notes I am looking at are located:
http://pillowlab.cps.utexas.edu/teaching/CompNeuro10/slides/slides16_EntropyMethods.pdf

On the bottom of slide 4 they get p_j = e^{1-λ} which is clear to me.

The next line says = 1/N.

I am having trouble understanding how they get to 1/N, from my understanding the N should represent the number of micro states however I don't understand how they jump from e^{1-λ} to 1/N.

Would anyone be able to clarify this for me?

Thank you,

 

[clamtrox]

The probability is the same for all j, so therefore you have $\sum p_i = 1 = N p_i$.