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Given the context I think that this sentence means "it's probably an unintentional action".
But I am unsure of what meaning/nuance the うち adds here. I am used to seeing うち meaning "while" and that's what I'm seeing on various internet sources. But I don't see how a "while" fits into this sentence.
In that context, 「うち」 refers to the situation in which an action is performed or an event takes place.
"While" would not always work as a translation. In fact, I feel that you are thinking of another usage of 「うち」 which describes temporal relationships.
「Intangible Noun + の + うち + の + Noun」
= "(Noun) taking place in the situation described by (Intangible Noun)"
「[無意識]{むいしき}のうちの[行動]{こうどう}」 = "an action performed in (the realm of) unconsciousness"
「Intangible Noun + の + うち + に + Verb Phrase」
「オリンピックは[成功]{せいこう}のうちに[終]{お}わった。」 = "The Olympics ended in success"
Goo辞書 entry #4 under うち【内】 had this to say:
４ （「裡」とも書く。「…のうちに」の形で）物事の行われる状況を表す。「暗黙の―に理解しあう」「会は成功の―に終わる」
4 (Also rendered 「裡」; Used in the form 「...のうちに」) Denotes the conditions in which something is done (*I'll come back to the examples later.)
Although the dictionary for some reason only mentions the adverbial form 「...のうちに」, the adnominal form 「...のうちの」 is also in use, though perhaps with less occurrence. (e.g.「暗黙のうちの了解」,「知らず知らずのうちのマナー違反」 )
With this in mind, let's look at your sentence 「無意識のうちの行動なのだろう」.
The adnominal 「のうちの」 relates 「行動(an action)」 to 「無意識(unawareness, unintentional-ness)」 .
「無意識」 is the state, or condition, within whose notional "boundaries" the 行動 was taken. The action was done, so to speak, in the territory of unawareness.
Notably, the English preposition in has a very similar meaning to this use of うちに.
In:
- With reference to circumstances or conditions
or
- With reference to physical surrounding, personal states, etc., abstractly denoted
(Both cited from here.)
To illustrate using the examples from goo辞書:
暗黙のうちに理解しあう ⇔ understand each other in silence
会は成功のうちに終わる ⇔ the meeting/gathering ends in success
In the two examples above, both ~のうちに and in describe in what way or under what circumstances/conditions something happens. However, this does not mean they are always the best translation for each other. For instance, "tacitly" would be a better word for「暗黙のうちに」 most of the time.
「無意識のうち」is an expression, actually.
You can find out more of the specific meanings in http://thesaurus.weblio.jp/content/無意識のうちに
It is still the same "while" meaning, but in English it is not translated that way, since the while is implied. "It was probably done while not being aware" would be the literal translation.
Just like ShikiGami said, it also means "while" here. You can translate it to something like... "It must be/must have been probably a behavior taken "while" being in one's unconscious mind." Hope this helps a bit...
うち in this case indicates a period within which an action is happening; so "inside the time". In English you would probably translate it as "while still".
While your translation sounds correct, in the Japanese sentence the fact that the action is unintentional/unconscious gets emphasized a bit more. To bring that out in the translation, you could maybe say: "It was probably an unconscious action/action made unconsciously."
