Why weights in systematic resampling algorithm are set to (1/N)?

Question

I am studying particle filtering algorithm. And this algorithm says that to overcome degeneracy problem, we have to apply resampling algorithm. In this resampling algorithm, it is stated that

After resampling, the weights are set to 1/N because by drawing according to the importance weight, one replaces 
“likelihoods” by “frequencies”

I am not understanding the meaning of this line. Why do we need do to set weight = 1/N? Here is the LINK Page no. 31

Answer 1

Imaging having N particles spread over the area of a room. Only at two Places of this room (A and B), the preception results are fitting to the expectation. For the sake of simplicity, we assume that both positions results in equal weights, wherease every other position in the room does not comply to the perception results and therefore having a weight 0 zero. Thus, we have one particle at A with a weight of 0.5 and one at B with 0.5 (caused by normalizing the weigts to a sum of 1) which resambles the likelihood for the real position.

Now we resample N particles according to the weights and (in a perfect world and with some luck) end up with 0.5*N particles at A and 0.5*N particles at B, since a particle had a chance of 50% to end up at A. By setting the weights of all particles to 1/N, the sum of weights of all particles at A is 0.5*N * 1/N = 0.5. Same of B. Therefore, by resampling and reweighting the particles we still express the same distribution but not as likelihood (Higher probability for positions with a particle with higher weight) but as frequency (higher probability for places with a lot of particles = frequency )