How to input a given sequence to a transformer (or an RNN) with probability of occurrence?

I'm experimenting with music and transformers, and I have sequences $$S$$ of shape: $$(B,L,N)$$ where $$B$$ is the batch size, $$L$$ is the sequence length, and $$N=12$$ are the number of musical notes with each $$N_i , i\in[0,11]$$ representing the probability of each note. i.e. $$\sum_{i=0}^{N-1}N_i=1$$

I also have embeddings $$E$$ for each note of shape: $$(N,512)$$

1. Then I take $$\text{argmax}_N (S)$$ which gives most probable note of shape: $$(B,L)$$

2. then pick the corresponding embedding (gather in tensorflow), resulting in shape: $$(B,L,512)$$ which I feed to the transformer, I'll call this $$X$$

3. I also take the probability $$P$$ of the most probable note by taking $$\text{max}_N (S)$$, shape: $$(B,L)$$

4. Now I feed $$X$$ to a transformer (or an RNN), but the problem is the transformer (or an RNN) doesnt take the probability of occurrence of that note into account.

5. I was thinking of ways to include the probability aswell along with the embeddings, and I'm thinking of taking the direct product of $$X$$ and $$P$$ (resulting shape: $$(B,L,512)$$) and then feed this to the transformer, i.e. multiplying each note embedding with its occurrence probability

Question: It is okay to give the multiplied embedding ($$XP$$) to the transformer or an RNN?

I'm guessing it is okay because the dot products $$(QK^T)$$ in a transformer is simply scaled to the given probability

P.S: I'm note sure whether this question fit in AI S.E or DataScience S.E, feel free to move this question, if required.

Thanks