Construction

THE CHANCES OF rather than THE CHANCES FOR; and MY is probably redundant, depending on the context.

Other than that, it sounds perfectly adequate English.

Hmm. Let's look at this...

"The chances of my ever being interrogated were nil...." Dave is right, "chances of."

"...but I nevertheless felt better that way." Try "...but I felt better that way" or "...nevertheless, I felt better that way."

Even so. What I think you are trying to get across is that someone who thought they were going to be interrogated (this is a bad thing, yes?) is relieved to find that it is probably not going to happen.

But what your sentence actually implies is that the person is somewhat surprised to find that he feels better, despite having to miss the interrogation that he wanted. Is that what you meant?

" nevertheless I felt " gets 2,380 hits on google.
"I nevertheless felt " gets only 680, but one of them is from Melville.

Speedwell, what is it that bothers you exactly? "I nevertheless felt ", today, does it sound : oldfashioned, affected, or just plain weird?

Here is what I meant: "I didn't take any maps, nor any notes about the places we went to. I had been told I would be taken to secret places, and I didn't want to remember their names nor the way to get to them. What you don't know, you can't tell. The chances of my ever being interrogated were nil, but I nevertheless felt better that way."

Thanks for the of!

I think that it isn't entirely clear what "that way" refers to. Also, when you say "taking" maps and notes, do you mean taking them with you when you went places, or making them when you went places?

It sounds awkward to have both "any"s in your first sentence, since the second one would be assumed if you omitted it ("I didn't take any maps or notes. . .").

Not to impose my style on your writing, but it might be clearer if you tried something like:

I took neither maps nor notes about the places we went to. I had been told I would be taken to secret places, and I wanted to remember neither their names nor the way to them. What you don't know, you can't tell. There was no chance of my ever being interrogated, but such precautions made me feel better.

But clarity is not always the only goal in writing :)

Oh, I should have clarified. "But" and "nevertheless" mean the same thing. It is redundant to use both. I would choose one or the other.

but/nevertheless, got it.

"But clarity is not always the only goal in writing".
How very true! And how very fantastic is English: you can be as precise as you want, or as ambiguous as you wish!