1. The standard story

In ordinary logical discourse, the words 'conclusion' and 'supposition' mean something quite different from what you here propose. To say that Jeff concludes C (from premises [math]\Gamma[/math]) is just to say that he makes the following assertion: [math]\Gamma \vdash C[/math]. This will be true just in case C follows from [math]\Gamma[/math], where what follows from what is determined by the particular definition of the consequence relation [math]\vdash[/math]. To say that Jeff supposes S is just to say that he assumes S to be true in order to reach certain conclusions.

2. Your account

a. Your first and last paragraphs indicate that you think of supposition and conclusion differently than I described above. You associate concluding with "deciding", and supposing with "guessing", leaving those terms undefined. Now let's look at your definitions. To say that Jeff concludes C is just to say that Jeff asserts that C. This effectively reduces your notion of conclusion to that of assertion, rendering it redundant, because every time you say "x concludes y", you can just say that x asserts y or that x says that y, and so on.

b. In your reply to Tiago's answer, you expressed your familiarity with modalities, so I'll allow myself to use basic modal-logical notions in trying to indicate what's missing from your proposal. Here's your attempt at defining supposition. To say that Jeff supposes S is just to say that Jeff asserts that [math]\Box[/math](S), where the box is to be understood as the "should" operator. Now, there are different flavors of "should"; some examples: (i) according to the weather report, it should rain tonight, (ii) according to Peano's axioms, zero should not have a predecessor, (iii) given all we've learned about the Moon, there shouldn't be any life on it, and so on.

3. Your task

In order for your definition of supposition to be acceptable, you need to specify which definition of 'should' you're taking. Depending on your choice, different modal-logical axioms will have to be chosen so that the appropriate conclusions can be drawn. As it stands, your use of the word "should" is ambiguous. But I trust that your knowledge of the modalities will come in handy in disambiguating it. Further, you need to define what you mean by "certainty"; until then, I'm going to not pay attention to "I'm very certain" in your example. Now the example.

4. The example

Given your account of conclusion as assertion (see 2a), and the problem with your definition of supposition (see 2b, 3), your example demonstration doesn't go through. Let M denote the sentence "life cannot exist on Mars". The example then says (I leave out the certainty part, because that's not defined; see 3 above):

T1: Jeff [asserts] that M
T2: ~M
T3: Jeff [had incorrectly] supposed that M

From (T1-2) follows that Jeff was wrong to assert that M. But (T3) is claiming that: (i) Jeff had supposed that M, and that (ii) Jeff's supposition that M was wrong. If Jeff had in fact supposed M, given T2, his supposition would in fact be wrong. But how does Jeff's supposition follow from T2 and T1? That's the question that you need to address. When you explicate your account of "should", we'll then be able to judge whether that supposition claim follows from (T1-2) or not.