Why PEP is the average power during one RF cycle at the crest of the modulation envelope. An unmodulated carrier is a steady sine wave whose envelope never changes, so the peak envelope cycle is the same as every other cycle and PEP equals the average power. The ratio is therefore exactly 1.00. Only when modulation makes the envelope rise and fall (as in SSB voice) does PEP exceed average power.
Watch out The 0.707 and 1.414 values are the RMS-to-peak conversion factors for instantaneous voltage or current on a sine wave, not a power ratio, and they do not apply to comparing PEP with average power.
Flat envelope, no peaks: unmodulated carrier means PEP = average, ratio 1.00.