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

Question

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