Construct Multinomial conditional distributions, where total_count is a random variable

I am trying to build a graphical model in Tensorflow Probability, where we first sample a number of positive (1) and negative (0) examples (count_i) from Categorical distribution and then construct Multinomial distribution (Y_i) depending on the value of (count_i). These events (Y_i) are mutually exclusive :

Y_1 ~ Multinomial([.9, 0.1, 0.05, 0.05, 0.1], total_count = [tf.reduce_sum(tf.cast(count==1, tf.float32))

Y_2 ~ Multinomial([0.99, 0.01, 0., 0., 0.], total_count = [tf.reduce_sum(tf.cast(count==0, tf.float32))

I have read these tutorials, however I am stuck with two issues:

1. This code generates two arrays of length 500, whereas I only need 1 array of 500. What should I change so we only get 1 sample from Categorical distribution and then depending on the overall count of the value we are conditioning on, Multinomial is constructed ?
2. The sample from Categorical distribution gives only values of 0, whereas it should be a blend between 0 and 1. What am I doing wrong here?

My code is as follows. You can run these to replicate the behaviour:

    def simplied_model():
      return tfd.JointDistributionSequential([
          tfd.Uniform(low=0., high = 1., name = 'e'), #e
          
          lambda e: tfd.Sample(tfd.Categorical(probs = tf.stack([e, 1.-e], 0)), sample_shape =500), #count #should it be independent?
          lambda count: tfd.Multinomial(probs = tf.constant([[.9, 0.1, 0.05, 0.05, 0.1], [0.99, 0.01, 0., 0., 0.]]), total_count  = tf.cast(tf.stack([tf.reduce_sum(tf.cast(count==1, tf.float32)),tf.reduce_sum(tf.cast(count==0, tf.float32))], 0), dtype= tf.float32))
      ])

    tt = simplied_model()
    tt.resolve_graph()
    tt.sample(1)

Start with the simplied_model entry point and the referenced Multilevel Modeling Primer tutorial. Clarify the intended sample shape and conditional Multinomial behavior, then verify that one length-500 categorical sample and the requested conditional counts are produced as described.