If we reproduce the structures with simpler content, we have alternatives as below, for example in answer to the question Why did he do that?
He's probably [just tired].
He's just [probably tired].
He probably [just didn't think].
He just [probably didn't think].
If we replace just with a different adverb, we have alternatives such as:
He probably [never thought about it].
He never [probably thought about it].
He probably [already knows that].
He already [probably knows that].
For me, the first alternative in each case is the natural one.
My natural inclination is supported by The Cambridge Grammar of the English Language (p576). The CGEL distinguishes verb-phrase oriented adjuncts from clause-oriented adjuncts.
Verb-phrase oriented adjuncts, as the name suggests, modify verb phrases and are " ... likely to be positioned in the VP or adjacent to the VP." Clause oriented adjuncts "... are less closely associated with the VP constituents and less likely to be positioned in the VP or adjacent to the VP.
The CGEL follows by noting that the positioning of VP-oriented adjuncts:
... correlates with a semantic observation, namely that VP-oriented
adjuncts denote modifications of the details of the predicate of a
whereas clause-oriented adjuncts
... represent modifications to the applicabilty
of the clause content. That is, their semantic effect is to
characterise how the propositional content of the clause relates to
the world or the context: ... (including) the array of possible
situations within which it is true (modality).
The CGEL classifies just as an adverb of degree, and as such it belongs in the VP-oriented adjunct category. Probably, on the other hand, is a clause-oriented adjunct.
The CGEL then has a section entitled Adjunct orientation and linear position. It notes:
... if a clause-oriented adjunct AdvP and a VP-oriented adjunct are
both in the central position, they will be in that order, or will
acquire a different and perhaps unusual meaning if not in that order:
It probably sometimes fails.
?It sometimes probably fails
(The question mark indicates a construction of dubious grammaticality.)
In conclusion, it is worth noting CGEL's general comment about adjunct positioning:
Only rather broad and approximate flexible generalisations about
adjunct placement can be made. There is a great deal of variation in
use, and features of content, style, prodsody, and euphony play a role
in some decisions.