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"improbable occurrence" is both correct and usable in written English
You can use it whenever you are referring to something that is not likely to happen. For example: "The chances of a series of improbable occurrences all taking place at the same time are slim."
Exact(3)
The other day it proclaimed that the low would be 39 degrees, an improbable occurrence in August in Southern California, where I was.
One of the basic premises of the article is that "The fundamental question is whether 'life as we know it and its astonishing chemical complexity is a very improbable occurrence or a nearly inevitable evolution of dynamic off-equilibrium chemical matter.
Oparin's and Haldane's papers are included in the first book in the table by J. D. Bernal: "Origin of Life" The fundamental question is whether 'life as we know it' – its astonishing chemical complexity – is a very improbable occurrence or a nearly inevitable evolution of dynamic off-equilibrium chemical matter.
Similar(57)
To the contrary, these highly improbable occurrences are overwhelmingly, urgently, astoundingly real.
Standing in a new venue which was nearly closed down on its opening night, in a city brought to a standstill by a tube strike, watching a band who were shelved for five years thanks to their singer's breakout solo career, a series of highly improbable occurrences have coincided to throw together east London's huddled masses for tonight's show.
It culminated in comedian Norman Long's release of a comic song in 1933, ironically titled "On the Day That Chelsea Went and Won the Cup", the lyrics of which describe a series of bizarre and improbable occurrences on the hypothetical day when Chelsea finally won a trophy.
It is difficult to explain this change, but we deem highly improbable that the consecutive occurrence of these two clinical pictures could be simply coincidental: it is not rarely observed that aura could undergo modification during the natural history of the patients without a convincing explanation [7].
Based on my air travel history, that occurrence is improbable, but I really appreciate those types of well wishes.
We therefore find it improbable that the high occurrence and severity of motor problems in the ADHD group found in this study, was due to a biased sample.
It concerns the occurrence of the improbable, the power of rare events and the author's lament that "in spite of the empirical record we continue to project into the future as if we were good at it".
For example, a smoke ring (ordered configuration) diffuses into the air (random configuration); the spontaneous reverse occurrence is statistically improbable to the point of impossibility.
More suggestions(15)
impossible occurrence
unthinkable occurrence
rare occurrence
likely occurrence
improbable distribution
insignificant occurrence
plausible occurrence
questionable occurrence
improbable frequency
improbable problem
improbable phenomenon
improbable phenomena
improbable accounts
improbable situations
very unlikely occurrence
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com