def generate_proba_coeffs(noise_list, mult=1.):
  """Generates probability coefficients s.t `coeff*(beta_i-beta_j)=const`"""
  n_replicas = len(noise_list)
  betas = sorted([1/n for n in noise_list])
  diffs = [betas[i] - betas[i+1] for i in range(n_replicas - 1)]
  coeffs = [1.]
  for i in range(1, n_replicas - 1):
    coeffs.append(coeffs[i-1]*(diffs[i-1]/diffs[i]))

  return [c*mult for c in coeffs]