I came across these sentences in [a learner's dictionary](http://www.learnersdictionary.com/definition/can) (see examples for sense 3a) today:

> 
> Do you think he *can* still be alive? [= do you think it is possible that he is still alive.]
> 
> 
> I don't think he *can* still be alive. [= I think he must be dead.]
> 
> 
> 

Since the second one is negative, it's probably not wrong, as it's pretty much a paraphrase of *I think he can't still be alive.* and *can't* can be used with the sense of *0% probability*, i.e. can't = I'm certain it's not true.

The Problem
-----------

From what I've known and what I've read, *could*, but **not** *can*, is usually used this way to indicate *probability* either in the present or the future, as in *he coud be in the garden.*

As for possibility, *can* can only be used to tell general possibilities/truths (*It can be rainy here during September.*) or the possibility in a particular situation (We can go to Paris this weekend, since we don't have to work).

What I Think & What I've Tried Doing
------------------------------------

I think the first one should read

> 
> Do you think he could still be alive?
> 
> 
> 

and probably even the second one should read

> 
> I don't think he could still be alive.
> 
> 
> 

However, it seemed strange **to me** (who is a non-native) when I replaced *could* with *may* in the first sentence, which is usually possible when talking about probability.

> 
> \*Do you think he may still be alive?
> 
> 
> 

I also noticed that

> 
> Do you think he is still alive?
> 
> 
> 

seemed more natural.

The Questions
-------------

* What is *can* doing there?
* In what context is *can* used like this?
* Can *could* do the job too?

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**Note**

* I'm talking about using *can* and *could* in the present here. (This may lead to varying answers if I don't make this clear, I think)
* Please, please avoid the word "possible" where possible. If you're going to use it, please make it clear what *kind* of "possible" you mean: generally possible (he can be hard at times), possible in the situation (we can go to Paris this weekend because we don't have to work), possible as in *probability* (he could be in the car.)