Our own survival chances seem to be a fraction not close to unity, but not close to 0 either. Give it 75% to be optimistic. After that, robotic seed space ships could be a buffer to protect from subsequent cataclysms. That does nothing to answer the questions of Fermi's paradox, unless you low-ball to 1.0e-6% chance of survival. Doomsayers guessing such a number are not generally taken seriously.
Looking elsewhere, we have almost unlimited wiggle room in the chance of photosynthesis evolving. Traits that evolved multiple times in Earth's history are inadmissible to this discussion, but several critical traits evolved only once. Fertile but desolate planets are, based on current science, probably abundant. As a typical reasonable human, this is a perfectly sufficient speculative answer.
But I also know I'm missing out on the true space-faring age, the Humanitarian Revolution, the Quantum Age where we begin to fully exploit the laws of QM, the Last World War, extra-solar colonization, etc.
Eventually, if we don't kill or exhaust ourselves with impatience, technology will be solved with respect to providing enough energy and resources for every conceivable human. Then, the real challenge begins. Providing for a population beyond its basic needs becomes an entirely political affair. We may be arrested on the lower levels of Maslow's Hierarchy of Needs for quite some time.
Will humanity observe a similar exponential advancement in humanitarianism as it has with technology? How important is humanitarianism to Fermi's Paradox and the Drake Equation?