How can I get `reduce` to divide values in the stream by one another?

One should not use reduce with an accumulator function that is not associative. This has been especially highlighted in the JDK documentation of the API as well.

The accumulator function must be an associative function.

You don't really need to rely on streams for this manipulation, in fact, streams are not good in persisting intermediate states(as in this case), so a simple for loop solution shall work for you :

int reduce = 1;
for (Integer integer : List.of(3, 27)) {
    reduce = integer / reduce;
}
System.out.println(reduce);

To test out the inconsistency in terms of using the stream API for this purpose, just change your code to the following and notice the output!

Integer reduce = List.of(3, 7).parallelStream().reduce(1, (a, b) -> b / a);
System.out.println(reduce);

You have to swap a and b:

System.out.println (Stream.of(3,27).reduce(1, (a,b) -> b/a));

output:

9