The succinct answer is: when you have the conjunction que, splitting a whole phrase in tho parts, each one with its own verb, then the main one must be in the indicative mood, and the second one in the subjunctive mood.
So, the sentence you gave:
It is likely that he will continue to develop
Can be translated as:
Es probable que él continúe desarrollándose (o desarrollando).
Going a little further:
Using a phrase like es probable que, you have three main things to consider:
- That is a phrase in the present tense, and as is the main one, must be in indicative.
- Since it has a que conjunction, what follows it must be in subjunctive mood.
- Since the main verb is in present tense, the subordinated phrase (that is the name of those sentences following a que) must be in the same present tense, but in the subjunctive mood.
So, for instance we may have:
Es probable que Miguel aparezca esta tarde.
But: what happens when the main sentence is in imperfect? Well, in this case the subordinated phrase must also be in imperfect tense, in the subjunctive mood:
Era probable que Miguel apareciera esta tarde (ahora sabemos que no vendrá).