It's a DM call, but Augury can serve as an example
The Augury spell contains the same "random reading" text:
If you cast the spell two or more times before completing your next long rest, there is a cumulative 25 percent chance for each casting after the first that you get a random reading. The DM makes this roll in secret.
In Augury's case, the intent seems more clear-cut: there are four possible results, so if a random reading occurs, a DM will likely roll randomly for one of the four options:
- Weal, for good results
- Woe, for bad results
- Weal and woe, for both good and bad results
- Nothing, for results that aren't especially good or bad
However, Divination (despite using the same text) does not have a finite list of results. As a DM, I personally might still use Augury's results as an example (and roll a d4, describing results similar to the above). Or I might roll a d20 and make up results: higher=better for PC's, lower=worse for PC's (I use this method for a lot of things). Or you could just use whatever short phrase, cryptic rhyme, or omen comes to mind (making this even easier to DM than a normal Divination result).
For completeness (i.e. you didn't ask for it, but others might like to know), "cumulative 25 percent chance for each casting after the first" means:
- First casting: 0% chance of random reading
- Second casting: 25% chance of random reading
- Third casting: 50% chance of random reading
- Fourth casting: 75% chance of random reading
- Fifth+ casting: 100% chance of random reading