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Shuffle a subset of a list

Shuffle a subset of a list

<sup>Idea shamelessly stolen from [caird](https://chat.stackexchange.com/transcript/message/58238435#58238435) and [rak1507](https://chat.stackexchange.com/transcript/message/58238593#58238593)</sup>

Shuffle a subset of a list of unique, positive integers with uniform randomness, given the indices of that subset. For example, given the list \$[A, B, C, D, E, F, G, H]\$ and the indices \$[0, 3, 4, 5, 7]\$ (0-indexed), you would extract the list \$[A, D, E, F, H]\$, shuffle it, and insert the shuffled elements back according to the list of indices. Some possible results of this are (elements that stayed in place are bolded)
$$[H, \textbf{B}, \textbf{C}, D, A, E, \textbf{G}, F]$$
$$[A, \textbf{B}, \textbf{C}, D, E, F, \textbf{G}, H]$$
$$[F, \textbf{B}, \textbf{C}, E, A, H, \textbf{G}, D]$$.

## Rules

- Every possible rearrangement of the list should have a non-zero chance of being chosen.
- You may use zero- or one-indexing, but please specify which you use.
- The indices in the input are guaranteed to be unique and valid.
- This is code golf, so least number of bytes wins.


## Test cases

All of these examples use 0-indexing.
```
List
Indices
Possible output

[1,2,3,4,5,6,7]
[0,1,2,3,4,5,6]
[2,3,6,1,0,4,5], etc.

[1,2,3,4,5,6,7]
[0,2,4,6]
[3,2,7,4,5,6,1], etc.

[93,6,10,1,200,41,78,31,34,27]
[0,3,4,8,9]
[1,6,10,27,93,41,78,31,200,34], etc.
```