Explanation:

Explain 

The sentence given here shows a sequence or coherence. As Harry passed by the corridor he saw somebody. There is no contradiction between the statements. Thus use of ‘But’ is inappropriate here. Thus choice III gets eliminated and option A as well.

Choice IV ‘Nevertheless’ is contextually not making any sense. This makes option D and E incorrect.

Now left with ‘as’ and ‘and’. ‘As’ is very much appropriate here to denote the coherence of the events of passing by and looking someone.

As Harry squelched along the deserted corridor he came across somebody who looked just as preoccupied as he was.

Similarly ‘and’ can also be used to connect the sentences, as it carry forwards the flow of the event.

Harry squelched along the deserted corridor and came across somebody who looked just as preoccupied as he was.

As both connectors given as choices I and II are fitting well.

Hence option C is correct.