Seated mediation, as I've been taught to practice, is not about logical analysis. That said, when it comes to 'thinking the worst', the practice of attention recognizes that these are just thoughts. In a sense, it doesn't matter whether the events are likely or unlikely, because the thoughts are just thoughts. There can be value in rationally analyzing fears, but meditative practice starts with just observing the fears as they are, regardless of whether they are rational. When the whirlwind of doubt starts up again, just return to the object of meditation (often, the breath) and let things settle. This isn't easy, but that's why we practice.
A bit of an aside, but here is a passage from the Dhammapada, Mind (translation by Ananda Maitreya), that I think relates to this:
Just as an arrowsmith shapes an arrow to
perfection with fire,
So does the wise man shape his mind,
Which is fickle, unsteady, vulnerable, and
Like a fish taken from the safety of its watery
And cast upon the dry land
So does this mind flutter, due to the lure of the
Therefore one should leave the dominion of
How good it is to rein the mind,
which is unruly, capricious, rushing wherever
The mind so harnessed will bring one happiness.
A wise man should pay attention to his mind,
Which is very difficult to perceive.
It is extremely subtle and wanders wherever it
The mind, well-guarded and controlled,
Will bring him happiness.
One who keeps a rein on the wandering mind,
Which strays far and wide, alone, bodiless,
Will be freed from the tyranny of the tempter.
A man of fickle mind
Will never attain wisdom to its fullest,
Since he is ignorant of the Dhamma
And has wavering faith.
The heart of the fully conscious man
He has freed his mind of lust and anger,
He has transcended both good and evil.
Observe this body, as fragile as an earthen vase.
Build a mind as solid as a fortified city,
Then confront Mara with the weapon of
And (proceeding without attachment)
Guard what you have already conquered.
Certainly before long this body will lie on the
Lifeless and unconscious,
Cast aside like a useless log.
A mind out of control will do more harm
Than two angry men engaged in combat.
A well-directed mind creates more well-being
Than the wholesome actions of parents
Toward their children.